Ultimate GMAT Tool Kit: With CD-ROM; The Ultimate GMAT Advantage [1 ed.] 9780768914863, 0768914868

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About Thomson Peterson’s Thomson Peterson’s (www.petersons.com) is a leading provider of education information and advice, with books and online resources focusing on education search, test preparation, and financial aid. Its Web site offers searchable databases and interactive tools for contacting educational institutions, online practice tests and instruction, and planning tools for securing financial aid. Thomson Peterson’s serves 110 million education consumers annually.

For more information, contact Thomson Peterson’s, 2000 Lenox Drive, Lawrenceville, NJ 08648; 800-338-3282; or find us on the World Wide Web at www.petersons.com/about. © 2004 Thomson Peterson’s, a part of The Thomson Corporation Thomson Learning™ is a trademark used herein under license. Editors: Mandie Rosenberg and Joe Ziegler; Production Editor: Alysha Bullock; Composition Manager: Gary Rozmierski; Manufacturing Manager: Ray Golaszewski; Cover and Interior Design: Allison Sullivan. ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution, or information storage and retrieval systems—without the prior written permission of the publisher. For permission to use material from this text or product, submit a request online at www.thomsonrights.com Any additional questions about permissions can be submitted by e-mail to [email protected] ISBN 0-7689-1486-8 Printed in the United States of America 10

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Petersons.com/ publishing Check out our Web site at www.petersons.com/publishing to see if there is any new information regarding the test and any revisions or corrections to the content of this book. We’ve made sure the information in this book is accurate and up-to-date; however, the test format or content may have changed since the time of publication.

Credits “ The American Renaissance,” by James S. Turner, H um anities, Vol.13, N o. 2 (M arch/April 1992). Published by The N ational Endowment for the H umanities. “ Arnold’s Double-Sided Culture,” by John P. Farrell, H um anities, Vol. 12, N o. 3 (M ay/June 1991), pp. 26–30. Published by The N ational Endowment for the H umanities. “ The Artful Encounter,” by Richard Wendorf, H um anities, Vol. 14, N o. 4 (July/August 1993), pp. 9–12. Published by The N ational Endowment for the H umanities. “ The Debate O ver M ozart’s M usic,” by N eal Z aslaw, H um anities, Vol. 14, N o. 5 (September/ O ctober 1993), pp. 26–27. Published by The N ational Endowment for the H umanities. “ ‘I Am Christina Rossetti,’ ” by Antony H . H arrison, H um anities, Vol. 14, N o. 4 (July/August 1993), pp. 33–37. Published by The N ational Endowment for the H umanities. “ Images of Dorothea Lange,” by Therese Thau H eyman, H um anities, Vol. 14, N o. 5 (September/ O ctober 1993), pp. 6, 8–10. Published by The N ational Endowment for the H umanities. “ Large Format Expands L ittle Buddha,” by Bob Fisher, A m erican Cinem atographer, Vol. 75, N o. 5 (M ay 1994), p. 41. Reprinted by permission of A m erican Cinem atographer.

Contents 123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ABOUT THIS TOOL KIT. . . . . . . . . . . . . . . . . . . . . . . 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O h, the Sidebars You’ll See. . . . . . . . . . . . . . . . . . . . . 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 PART I: EVERYTHING YOU EVER WANTED 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 TO KNOW ABOUT THE GMAT 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Chapter 1: The GMAT—In a N utshell . . . . . . . . . 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Chapter 2: The GMAT—Up Close . . . . . . . . . . . . 41 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 PART II: ANALYTICAL WRITING 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ASSESSMENT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Chapter 3: Analytical Writing Assessment . . . . . . 72 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 103 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PART III: QUANTITATIVE ABILITY 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 4: Problem Solving . . . . . . . . . . . . . . . . . . 136 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 152 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 5: Data Sufficiency . . . . . . . . . . . . . . . . . . 164 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 177 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 6: Math Review—N umber Forms, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Relationships, and Sets . . . . . . . . . . . . . . . . . . . . 190 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 214 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 7: Math Review—N umber Theory and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 258 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 8: Math Review—Geometry . . . . . . . . . . 279 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 303 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PART IV: VERBAL ABILITY 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Chapter 9: Critical Reasoning . . . . . . . . . . . . . . . . 332 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 357 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 v

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Chapter 10: Sentence Correction . . . . . . . . . . . . . . 380 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 406 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Chapter 11: Reading Comprehension . . . . . . . . . . 429 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Take It to the N ext Level. . . . . . . . . . . . . . . . . . . 445 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PART V: THREE PRACTICE TESTS 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answers and Explanations . . . . . . . . . . . . . . . . . 497 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Answers and Explanations . . . . . . . . . . . . . . . . . 537 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answers and Explanations . . . . . . . . . . . . . . . . . 577 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 PART VI: APPENDIX 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Determining Your Score . . . . . . . . . . . . . . . . . . . . . . 594 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 vi www.petersons.com

About This Tool Kit 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Tools Your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Peterson’s Ultim ate G M AT Tool Kit provides the complete package you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to score your personal best on the GM AT and get into your 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 top-choice M BA program. Unlike any book previously published, this tool 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 kit contains many features that used to be available only to those who 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 purchased expensive test-prep classes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 e-Tutoring 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use the CD to go online to register for one-to-one math help from a live 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expert when you need it. Tutoring is offered using an online white board 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shared by you and the tutor that allows you to communicate with one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another in real time. H owever, if you prefer, you can submit your math 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question instead and receive an answer within 24 hours. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The free tutoring offered with this product is limited to 30 minutes, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 although you may purchase more time if you need it. A written response to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a submitted questions counts as 20 minutes. The tutoring service is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 available for six months from the date you register online. The e-tutoring 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 service offered to purchasers of this 2005 edition will expire on January 1, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2006. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 This service is available 24 hours a day seven days a week for most of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 year. During the summer it is available from 9 a.m. to 1 a.m. Eastern time. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Due to low demand, the service is not available during several holiday 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 periods including Thanksgiving, Christmas, and Easter, Labor Day, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M emorial Day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Remember, to register for this service you will need the CD that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 accompanies this book. You will also need to refer to this book to provide 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the access code when prompted. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 1

A bout T his Tool Kit

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Essay Scoring 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The CD that accompanies this book allows you to go online to write 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 practice test essays online and receive a score for each of them that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 approximates your performance on the essays in the actual GM AT. In 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 addition to a score, you will also receive constructive feedback on your 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 essays, including tips to improve your score. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 With this tool kit, you get scoring for 2 practice test essays—one analysis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of an issue and one analysis of an argument. If you wish, for a fee, you may 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 obtain scoring information and feedback for additional practice essays 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you write online. Please note: Your practice test essays will be scored by a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 computer, but for the actual GM AT test, the essays are scored by a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combination of a computer program and a human scorer. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To register for this essay-scoring service you need the CD that accompanies 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this book. In addition, you will need to refer to this book to provide the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 access code when prompted. The scoring of 2 essays is offered free to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 purchasers of the 2005 edition and this offer will expire on December 31, 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2005. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Computer-Adaptive Tests on CD 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The actual GM AT is a computer-adaptive test (CAT)—the test questions 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you so depend on your performance on previous questions. O n the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CD-RO M that accompanies this book, you will receive 3 practice GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CATs that carefully reproduce the experience you can expect on test day. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The additional three practice tests in the book can be used for further 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 practice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 About This Book 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O f course, another tool in your Ultim ate G M AT Tool Kit is this book 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 itself. It is structured so that you gain proven test-taking strategies to do 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your best on the exam, a thorough review of all content on the GM AT, and 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a complete understanding of how to attack the GM AT essays. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Part I: Everything You Ever Wanted to Know 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about the GMAT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Part I focuses on the “ big picture.” H ere you’ll learn about the overall 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 structure of the GM AT and what the test sections cover. You’ll also 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 examine the directions for each type of question and see what typical test 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions look like. Then, you’ll learn strategies for GM AT preparation as 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 1 well as general test-taking strategies. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

About This Book

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Parts II–IV: Study Guides for the GMAT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This book’s GM AT study guide is unique in that it offers you the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opportunity to study each part of the exam, and then you can Tak e It to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the N ex t L evel— using the section in each chapter that covers advanced 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 topics and concepts you may encounter on the GM AT. Each section covers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 all four test sections and all general question types and both contain 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 example questions. The unique ability to Tak e It to the N ex t L evel feature 2 2 12345678901234567890123456789012123456789012345678901 will help you tailor your GM AT prep to your individual needs. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Should You Take it to the Next Level? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 You should start with the general instruction if either of the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 describes you: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You’re a GM AT “ newbie” and you are just beginning your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT prep. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The B-school you want to attend doesn’t require especially high 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT scores for admission. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can go directly to Tak e It to the N ex t L evel if you’re a repeat GM AT 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 test-taker whose scores were high the first time around but your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT goals are now even higher. O f course, regardless of your goals for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the GM AT and for college admission, you can always work through both 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 levels. In fact, that’s what we recommend to anyone with enough study 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time before exam day. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Part V: Three Practice GMATs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Part V, you’ll find three full-length, practice GM ATs. Each test covers all 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four test sections and includes a mix of easy, moderate, and difficult 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questions. To accurately measure your performance on the practice tests, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be sure to adhere strictly to the time limits for each and every section. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can take all three practice tests after completing your self-study (Parts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 II–IV). O r, you can take one practice test beforehand as a diagnostic tool. 2 2 12345678901234567890123456789012123456789012345678901 th 2 12345678901234567890123456789012123456789012345678901 If your scores show that you rank above the 80 percentile on a test, you 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 can skip over the basics to Tak e It to the N ex t L evel for that test. Then, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 after you’ve completed your self-study, take the remaining two practice 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 tests to measure your improvement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

3

A bout T his Tool Kit

X-Ref

Tip

N ote

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Oh, the Sidebars You’ll See 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Throughout this book you’ll encounter four different types of sidebars. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Flip through this book, and you’ll see oodles of each one.) H ere’s a look at 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the types of sidebars you’ll see: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Warns you about a common testing trick or ploy that might 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 trip you up during the test if you’re not careful. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Signals information that may not be a “ need-to-know” fact, 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 but that you might find rounds out your knowledge of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 topic at hand. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Signals a tip, strategy, or fine point related to the topic or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example at hand. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Signals a reference to a concept or other information located 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 elsewhere in the book. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

4

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PART

I Everything You Ever Wanted to Know about the GMAT The GM AT—In a N utshell The GM AT—Up Close

6 41

PART I

Chapter

1 The GMAT—In a N utshell 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your GM AT prep begins with an overview of the test. In this chapter, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn Key acronyms related to the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Look at the overall structure of the GM AT and what each of the 2 12345678901234567890123456789012123456789012345678901 four test sections cover. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Familiarize yourself with the computerized aspects of the test. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Examine the directions for each for each general question type. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • See what typical test questions look like. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Find out how the GM AT is scored and evaluated. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Find out how your scores are reported to the business schools. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn strategies for GM AT preparation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn general GM AT test-taking strategies. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Key Acronyms 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. GMAT (G raduate M anagem ent A dm ission Test): This standardized 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test provides graduate business schools (as well as vocational 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 counselors and prospective applicants) with predictors of academic 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 performance in M BA programs. Approximately 850 graduate 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 business schools worldwide require GM AT scores for admission. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Another 450 graduate business schools use—but don’t require— 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GM AT scores to access applicants’ qualifications. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. GMAC (G raduate M anagem ent A dm ission Council): This organiza- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion develops guidelines, policies, and procedures for the graduate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 business school admission process, and provides information about 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the admission process to the schools and to prospective applicants. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GM AC consists of representatives from more than 100 graduate 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 business schools. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 6

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. CAT (Com puter-A daptive Test): Except for some locations outside of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N orth America, the GM AT is now offered only by computer. CAT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refers to the computerized version of the GM AT. Taking a computer- 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 adaptive test means that each section of the test starts with a question 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of moderate difficulty. If you answer correctly, the computer will 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 follow it with a more difficult question. If you answer it incorrectly, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the following question will be easier. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GMAT at a Glance 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GM AT contains three parts: an Analytical Writing Assessment 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 section, a Q uantitative Ability section, and a Verbal Ability section. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 total testing time (excluding breaks) is 3 hours, 30 minutes. H ere’s the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basic structure of the test: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 AN ALYTICAL WRITIN G ASSESSMEN T (Sections 1 and 2) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Analysis of an Issue (1 writing task, 30-minute time limit) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Analysis of an Argument (1 writing task, 30-minute time limit) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O ptional break (5-m inute tim e lim it) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 QUAN TITATIVE ABILITY (Section 3) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (37 multiple-choice questions, 75-minute time limit) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Problem Solving (22–23 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Data Sufficiency (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O ptional break (5-m inute tim e lim it) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 VERBAL ABILITY (Section 4) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 (41 multiple-choice questions, 75-minute time limit) 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Critical Reasoning (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Sentence Correction (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Reading Comprehension (12–13 questions, divided among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four sets) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sequence of Exam Sections 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Sections 1 and 2 (the two timed essay sections) always appear first (in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 either order), before the two timed multiple-choice sections. Section 3 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is always Q uantitative Ability, and section 4 is always Verbal Ability. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

7

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Sequence of Questions in Quantitative and Verbal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In each of the two multiple-choice sections, question types are 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interspersed. H ere’s a typical sequence for each section (on your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT, the sequence might be different): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 Quantitative Ability (Typical Sequence of Questions) 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 1–2 Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 3–7 Data Sufficiency 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 8–13 Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 14 Data Sufficiency 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Q uestion 15 Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 16 Data Sufficiency 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 17–21 Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 22–27 Data Sufficiency 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 28–34 Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 35 Data Sufficiency 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 36–37 Problem Solving 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Verbal Ability (Typical Sequence of Questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 1–3 Sentence Correction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 4–5 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 6–8 Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 9 Sentence Correction 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 10–11 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 12–14 Sentence Correction 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 15–17 Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 18–21 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 22–24 Sentence Correction 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 25–26 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestion 27 Sentence Correction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 28–30 Reading Comprehension 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 31–33 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 34–35 Sentence Correction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestions 36 Critical Reasoning 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestions 37–39 Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uestion 40 Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 41 Sentence Correction 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 1: The GM AT—In a N utshell

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Ground Rules 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are some basic procedural rules for the GM AT (later in this chapter 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 we’ll cover test-taking procedures in greater detail): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O nce the timed test begins, you cannot stop the testing clock. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If you finish any section before the time limit expires, you have the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 option of proceeding immediately to the next section. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O nce you exit a section, you can’t return to it. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Pencils and “ scratch” paper are provided for all exam sections. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • You select a multiple-choice answer by clicking on an oval next to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the choice. (All multiple-choice questions include five answer 2 12345678901234567890123456789012123456789012345678901 choices.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You compose both essays using the word processor built into the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT testing system. (H andwritten essays are not permitted.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Four Timed GMAT Sections 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a quick look at what each of the four timed test sections covers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Later in this chapter, you’ll see example questions in all of the formats 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 described here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis of an Issue (1 Essay, 30 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This 30-minute section tests your ability to present a position on an issue 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 effectively and persuasively. Your task is to compose an essay in which you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 respond to a brief (1–2 sentence) opinion about an issue of general 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 intellectual interest. You should consider various perspectives, and take a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position on the issue and argue for that position. Your essay will be 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 evaluated based on content, organization, writing style, and mechanics 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (grammar, syntax, word usage, etc.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis of an Argument (1 Essay, 30 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This 30-minute section is designed to test your critical-reasoning and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 analytical-writing skills. Your task is to compose an essay in which you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 critique a paragraph-length argument based on the strength of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evidence presented in support of it and on the argument’s logic (line of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 reasoning). You can also indicate what additional evidence would help you 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 evaluate the argument and how the argument could be improved. Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your Issue-Analysis essay, your Argument-Analysis essay will be evaluated 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 based on content, organization, writing style, and mechanics. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Quantitative Ability (37 Questions, 75 Minutes) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 This 75-minute section consists of 37 multiple-choice questions designed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to measure your basic mathematical skills; understanding of basic 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 mathematical concepts; and ability to reason quantitatively, solve quanti- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tative problems, and interpret graphical data. The Q uantitative Ability 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 section covers the following topics: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Arithmetical operations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Integers, factors, and multiples 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The number line and ordering 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Decimals, percentages, ratios, and proportion 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Exponents and square roots 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Descriptive statistics (mean, median, mode, range, standard 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deviation) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Basic probability, permutations, and combinations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O perations with variables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Algebraic equations and inequalities 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Geometry, including coordinate geometry 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Algebraic concepts on the GM AT are those normally covered in a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first-year high school algebra course. The GM AT does not cover more 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 advanced areas such as trigonometry and calculus. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each Q uantitative question appears in one of two formats (any of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 topics listed above is fair game for either format): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PROBLEM SOLVIN G questions require you to solve a mathematical 2 2 12345678901234567890123456789012123456789012345678901 problem and then select the correct answer from among five answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices. Some of these questions will be “ story” problems—cast in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 real-world setting. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 DATA SUFFICIEN CY problems each consist of a question followed 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by two statements labeled (1) and (2). Your task is to analyze each of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two statements to determine whether it provides sufficient data to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question and, if neither suffices alone, whether both 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statements together suffice. Every D ata Sufficiency question includes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the sam e five answ er choices. As with certain Problem Solving 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 questions, some of these questions will be so-called “ story” problems— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cast in a real-world setting. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Verbal Ability (41 Questions, 75 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This 75-minute section consists of 41 multiple-choice questions. Each 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 question will be one of the following three types (each type covers a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinct set of verbal and verbal-reasoning skills): 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 CRITICAL REASON IN G questions measure your ability to under- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 stand, criticize, and draw reasonable conclusions from arguments. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Each argument consists of a brief one-paragraph passage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 SEN TEN CE CORRECTION questions measure your command of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the English language and of the conventions of Standard Written 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 English. Areas tested include grammar, diction, usage, and effective 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expression (but not punctuation). In each question, part (or all) of a 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence is underlined. Your task is to determine which is correct—the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original underlined part or one of four alternatives. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 READIN G COMPREHEN SION questions measure your ability to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 read carefully and accurately, to determine the relationships among the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 various parts of the passage, and to draw reasonable inferences from 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the material in the passage. You’ll encounter four sets of questions; all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questions in a set pertain to the same passage. The passages are drawn 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 from for a variety of subjects, including the humanities, the social 2 12345678901234567890123456789012123456789012345678901 sciences, the physical sciences, ethics, philosophy, and law. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your GMAT Scores 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll receive four scores for the GM AT: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. A scaled Q uantitative score on a 0–60 scale 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. A scaled Verbal score on a 0–60 scale 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. A total score, on a 200–800 scale, based on both your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uantitative and Verbal scores 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. An AWA score on a 0–6 scale, which averages (to the nearest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one-half point) the final scores for each of your two GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essays 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For each of these four scores you’ll also receive a percentile rank (0–99% ). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A percentile rank of 60% , for example, indicates that you scored higher 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than 60% (and lower than 40% ) of all other test-takers. Percentile ranks 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 11

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 reflect your performance relative to the entire GM AT test-taking 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 population during the most recent three-year period. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Part IV, you’ll find tables that convert scaled scores to percentile ranks. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 How the Quantitative and Verbal Sections 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Are Scored 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The scoring system for the Q uantitative and Verbal sections is a bit tricky. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your score for each of these two sections is based on three factors: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The num ber of questions you answer correctly 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The difficulty level of the questions you answer correctly 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The range of question types and topics among the questions you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer correctly 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 So, even if you don’t respond to all 37 Q uantitative (or 41 Verbal) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions, you can still attain a high score for the section if a high 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percentage of your responses are correct—especially if you respond 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correctly to a wide variety of question types. The CAT system’s scoring 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 algorithms are well-guarded ETS secrets; however, knowing exactly how 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the system works wouldn’t affect your exam preparation or test-taking 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strategy, anyway. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Some questions on each of your two multiple-choice sections won’t be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scored. The test-makers include unscored, “ pre-test” questions on the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT in order to assess their integrity, fairness, and difficulty. Some of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these questions might show up as scored questions on the GM AT in the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 future. Pre-test questions are mixed in with scored questions, and you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t be able to tell them apart—so don’t risk trying. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How the GMAT Essays Are Scored 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The evaluation and scoring system for GM AT essays is also a bit tricky. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Initially, one person will read and evaluate your Issue-Analysis essay, while 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a different person reads and evaluates your Argument-Analysis essay. Each 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reader will award a single score on a scale of 0–6 in whole-point intervals 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (6 is highest). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Readers apply a holistic scoring approach, meaning that a reader will base 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 his or her evaluation on the overall quality of your writing. In other words, 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 instead of awarding separate sub-scores for content, organization, writing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 style, and mechanics, the reader will consider how effective your essay is as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a w hole—accounting for all of these factors. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 All GM AT readers are college or university faculty; most teach in the field 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 of either English or Communications. Each reader evaluates your writing 2 12345678901234567890123456789012123456789012345678901 independently of other readers, and no reader is informed of other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 readers’ scores. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Scoring Criteria for the GMAT Essays 2 12345678901234567890123456789012123456789012345678901 All readers are trained by ETS in applying the same scoring criteria. H ere 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 are the essential requirements for a top-scoring (“ 6” ) Issue-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (note that you can attain a top score of 6 even if your essay contains minor 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 errors in grammar, word usage, spelling, and punctuation): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The essay develops a position on the issue through the use of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incisive reasons and persuasive examples. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The essay’s ideas are conveyed clearly and articulately. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. The essay maintains proper focus on the issue and is well 2 12345678901234567890123456789012123456789012345678901 organized. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. The essay demonstrates proficiency, fluency, and maturity in its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use of sentence structure, vocabulary, and idiom. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. The essay demonstrates an excellent command of the elements of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Standard Written English, including grammar, word usage, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spelling, and punctuation—but may contain minor flaws in these 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 areas. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere are the essential requirements for a top-scoring (“ 6” ) Argument2 12345678901234567890123456789012123456789012345678901 Analysis essay (notice that the last two requirements are the same as for a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 top-scoring Issue-Analysis essay): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The essay identifies the key features of the argument and analyzes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each one in a thoughtful manner. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The essay supports each point of critique with insightful reasons 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and examples. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. The essay develops its ideas in a clear, organized manner, with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appropriate transitions to help connect ideas. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. The essay demonstrates proficiency, fluency, and maturity in its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use of sentence structure, vocabulary, and idiom. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. The essay demonstrates an excellent command of the elements of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Standard Written English, including grammar, word usage, 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 13

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 spelling, and punctuation—but may contain minor flaws in these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 areas. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The criteria for lower scores are the same as the ones above; the only 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difference is that the standard for quality decreases for successively lower 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scores. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The scoring criteria for all six score levels are published in the official 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 GM AT Bulletin as well as directly at the official GM AT Web site. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Computerized Rating of Your Two Essays 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 While two human readers evaluate your GM AT essays (one reader per 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay), a computer program called E-R ater® will evaluate your essays in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms of grammar, syntax (sentence structure), repetitiveness (overuse of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the same phrases), sentence length, and spelling. Like human readers, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E-Rater awards a score of 0–6 for each essay. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In many respects, E-Rater is similar to the grammar- and spell-checkers 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 built into popular word-processing programs such as Word and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 WordPerfect. H owever, E-Rater is custom-designed for ETS to weigh 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 certain criteria more heavily than others. For instance, very little weight is 2 2 12345678901234567890123456789012123456789012345678901 given to minor mechanical errors (e.g., in punctuation and spelling). Also, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E-Rater overlooks so-called “ gray” areas of grammar (e.g., use of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passive voice), and flags certain problems (e.g., repetitiveness) that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 off-the-shelf checkers might not. O f course, E-Rater is only useful to a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 point. It cannot evaluate your ideas or how persuasively you have 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 presented and supported those ideas. That’s what human readers are for. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 According to the testing service, the human readers’ and E-Rater’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combined evaluation takes into account more than 50 structural and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 linguistic criteria altogether. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Computation of Your AWA Score 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are the specific steps involved in calculating your AWA score: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. As mentioned above, one reader will read and score your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue-Analysis essay, and a different reader will read and score 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your Argument-Analysis essay. Each reader will award a single 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 score on a scale of 0–6 in whole-point intervals (6 is highest). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. E-Rater will also evaluate and award a score of 0–6 for each 2 2 12345678901234567890123456789012123456789012345678901 2 1 essay. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. For either essay, if the human reader’s score differs from E-Rater’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 score by more than one point, a second human reader will read 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and score the essay (and E-Rater’s score will be disregarded). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4. For each essay, your final score is the average of the scores 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awarded by the human reader and E-Rater (or by the second 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 human reader). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. You final AWA score is the average of your final scores for each 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 essay; AWA scores are rounded up to the nearest half-point. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 H ere’s an example showing how the AWA scoring system works: 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 4 Reader A’s evaluation of the Issue-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 E-Rater’s evaluation of the Issue-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 Reader B’s evaluation of the Issue-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3.5 Final score for the Issue-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 Reader C’s evaluation of the Argument-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 E-Rater’s evaluation of the Argument-Analysis essay 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 Final score for the Argument-Analysis essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3.5 AWA score 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice in this example that a second human reader evaluated the Issue 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Analysis essay, and that the average of the two final scores (3.25) has been 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rounded up (to 3.5). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Score Reporting 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O nce the GM AT readers have read and scored your two essays, ETS will 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 mail you an official score report for all four sections. (Expect your score 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 report within ten days after testing.) At the same time, ETS will transmit a 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 score report to each B-school you’ve designated to receive your score 2 12345678901234567890123456789012123456789012345678901 report. (You can direct reports to as many as five schools without charge.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 At this time, score reports don’t include the GM AT essays themselves, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 although ETS is working on it. Eventually, the CAT system will provide 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 disclosure of each test-taker’s complete exam (including the questions). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT absences and cancellations also appear on your official report, but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will not adversely affect your chances of admission. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 15

Part I: Everything You Ever W anted to Know about the G M AT

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How B-Schools Evaluate GMAT Scores 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each business school develops and implements its own policies for 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evaluating GM AT scores. Some schools place equal weight on GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scores and GPA, others weigh GM AT scores more heavily, whereas others 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weigh GPA more heavily. ETS reports your three most recent GM AT 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 scores to each business school receiving your scores and transcripts. M ost 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 schools simply average reported scores. (Q uantitative, Verbal, Total, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 AWA scores are each averaged separately for this purpose.) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A minority of schools have refined this approach by disregarding a score 2 2 12345678901234567890123456789012123456789012345678901 that is sufficiently lower than another score for the same ability—on the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 basis that the low score unfairly distorts the test-taker’s ability in this area. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O ther schools disregard all but your highest score of each type in any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 event. (This approach is increasingly uncommon, since it discriminates in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 favor of test-takers who can afford to take the GM AT repeatedly.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Any B-school will gladly tell you which method it uses among the three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mentioned above. But don’t expect any school to tell you exactly how 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 much weight it places on each exam section or on different admission 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 criteria (such as GM AT scores, GPA, work experience, and personal 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 statements). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How the Computer-Adaptive GMAT Works 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A “ computer-adaptive” feature of the GM AT CAT makes it an entirely 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 different animal than convention paper-based tests. The following are five 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 key features that set the CAT apart. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. During the two multiple-choice sections, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GMAT CAT will continually adapt to your ability 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 level. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The “ A” in CAT stands for “ Adaptive,” which means that during each of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two multiple-choice sections the testing system tailors its difficulty 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 level to your level of ability. H ow? The initial few questions of each type 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 are average in difficulty level. As you respond correctly to questions, the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CAT system steps you up to more difficult questions. Conversely, as you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond incorrectly to questions, the CAT steps you down to easier ones. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, the CAT builds a customized test for you, drawing on its very large 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 pool of multiple-choice questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 16 123456789012345678901234567890121234567890123456789012

N ote

Alert!

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Early in an exam section, the CAT can shift from the easiest level to a very 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 challenging level (or vice versa) in as few as 3 or 4 successive questions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But later in the section, when your ability level is well established, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficulty level will not vary as widely. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The GMAT CAT does not let you skip questions. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Given the adaptive nature of the test, this makes sense. The computer- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 adaptive algorithm cannot determine the appropriate difficulty level for 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the next question without a response (correct or incorrect) to each 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 question presented in sequence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 3. The GMAT CAT does not let you return to any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question already presented (and answered). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Why not? The computer-adaptive algorithm that determines the difficulty 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of subsequent questions depends on the correctness of prior responses. For 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 example, suppose you answer question 5 incorrectly. The CAT responds 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 by posing slightly easier questions. Were the CAT to let you return to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question 5 and change your response to the correct one, the questions 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 following question 5 would be easier than they should have been, given 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your amended response. In other words, the process by which the CAT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 builds your GM AT and determines your score would be undermined. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. The GMAT CAT does not require you to answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 all available questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The CAT gives you the opportunity to respond to a total of 37 2 12345678901234567890123456789012123456789012345678901 Q uantitative and 41 Verbal questions. But the CAT does not require you to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 finish either section. The CAT will tabulate a score regardless of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of available questions you’ve answered, except if you fail to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond to at least one question during a section, in which case an “ N S” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (no score) will appear on your score report for that section only. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During each of the two essay sections, if you fail to key in (type) at least 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one character using the CAT word processor, you’ll automatically receive 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a score of 0 (on a scale of 0 to 6) for that section; this score will appear on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your report. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 17

Part I: Everything You Ever W anted to Know about the G M AT

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. During each section, the GMAT CAT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 automatically warns you when time is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 running out. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When 5 minutes remain during each timed section, the on-screen clock (in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the upper left corner of the screen) will blink silently several times to warn 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 you. This 5-minute warning will be your only reminder. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Beepers and alarms aren’t allowed in the testing room, although silent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 timing devices are permitted. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 The GMAT CAT Interface 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The three simulated screen shots on pages 19, 21, and 22 show the GM AT 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 CAT interface for the AWA sections, the Q uantitative Ability section, and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Verbal Ability section. Let’s first examine the features of the interface 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that are common to all exam sections. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The CAT Title Bar 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A dark title bar will appear across the top of the computer screen at all 2 2 12345678901234567890123456789012123456789012345678901 times during all test sections. (You cannot hide this bar.) The CAT title bar 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 displays three items: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Left corner: The time remaining for the current section (hours and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 minutes) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Middle: The name of the test (GM AT) and current section number 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Right corner: The current question number and total number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions in the current section 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 18 123456789012345678901234567890121234567890123456789012

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ame and N umber 2 12345678901234567890123456789012123456789012345678901 CAT Title Bar of Text Section Time elapsed 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The following appeared in a memo from the manager of UpperCuts, a hair salon 2 12345678901234567890123456789012123456789012345678901 located in a suburb of the city of Apton, to the salon's owner: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 "According to a nationwide demographic study, more and more people today are 2 12345678901234567890123456789012123456789012345678901 AWA Topic moving from suburbs to downtown areas. So in order to boost sagging profits at 2345678901234567890123456789012123456789012345678901 2 1 UpperCuts we should relocate the salon from its current location in Apton's 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suburban mall to downtown Apton, while retaining the salon's decidedly upscale 2 12345678901234567890123456789012123456789012345678901 approach in terms of services, products and pricing. After all, HairDooz, our chief 2 12345678901234567890123456789012123456789012345678901 competitor at the mall, has just relocated downtown and is popular among 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The AWA 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Editing 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Screen 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext Confirm H elp Exit Q uit Time 2 12345678901234567890123456789012123456789012345678901 button button Answer Test Selection button 2 12345678901234567890123456789012123456789012345678901 button button button 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The CAT Toolbar 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A series of six buttons appear in a toolbar across the bottom of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 computer screen at all times during all test sections. (You cannot hide the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 toolbar.) H ere’s a description of each button’s function: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 QUIT TEST 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Click on this button to stop the test and cancel your scores for the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 entire test. (Partial score cancellation is not allowed in any event.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If you click here, a dialog box will appear on the screen, asking you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to confirm this operation. Stay away from this button unless you’re 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 absolutely sure you wish your GM AT score for the day to vaporize 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and you’re willing to throw away your GM AT registration fee. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 EXIT SECTION 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Click on this button if you finish the section before the allotted 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 time expires and wish to proceed immediately to the next section. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A dialog box will appear on the screen asking you to confirm this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 operation. Stay away from this button unless you’ve already 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 answered every question in the current section and don’t feel you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need a breather before starting the next one! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 19 00:28

Computer-Adaptive GMAT-Section 2:Analytical Writing 2

Beginning

The manager's argument relies on a series of unproven assumptions and is therefore unconvincing as it stands. To begin with, the argument assumes that Apton's demographic trend reflects the national trend. Yet, the mere fact that one hair salon has moved downtown hardly suffices to |

Cut

Paste

Undo

Test

Section

Quit

Exit

Answer

Time

Help

Confirm

Next

Part I: Everything You Ever W anted to Know about the G M AT

www.petersons.com

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 TIME 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Click on this button to display the time remaining to the nearest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 second. By default, the time remaining is displayed (in the upper 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 left corner) in hours and minutes, but not to the nearest second. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 HELP 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Click on this button to access the directions for the current 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question type (for example, Data Sufficiency or Sentence Correc2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion), as well as the general test directions and the instructions for 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 using the toolbar items. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N EXT and CON FIRM AN SWER 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Click on the N EXT button when you’re finished with the current 2 2 12345678901234567890123456789012123456789012345678901 question. When you click on N EXT, the current question will 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remain on the screen until you click on CO N FIRM AN SWER. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Until you confirm, you can change your answer as often as you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wish (by clicking on a different oval). But once you confirm, the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question disappears forever and the next one appears in its place. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Whenever the N EXT button is enabled (appearing dark gray), the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CO N FIRM AN SWER button is disabled (appearing light gray), 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and vice versa. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The AWA Screen 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 As illustrated in the screen shot on page 19, the AWA prompt appears at 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the top of your screen, and your essay response appears below it as you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 type your response. (The screen in the figure includes the first several lines 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of a response.) N otice that you have to scroll down to read the entire topic 2 2 12345678901234567890123456789012123456789012345678901 and question. You compose your essays using the CAT word processor. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Just ahead, you’ll look closely at its features and limitations.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The Quantitative and Verbal Screens 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To respond to multiple-choice questions, click on one of the ovals to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the left of the answer choices. You can’t use the keyboard to select 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answers. N otice that the answer choices are not lettered; you’ll click on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 blank ovals. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the sample questions throughout this book, the answer choices are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lettered for easy reference to corresponding explanations. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Split screens. For some multiple-choice questions, the screen splits 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 either horizontally or vertically. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 R eading Com prehension: The screen splits vertically. The left side 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 displays the passage; the right side displays the question and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Q uantitative questions that include figures: The screen splits 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 horizontally. The figures appears at the top; the question and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices appear at the bottom. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Vertical Scrolling. For some multiple-choice questions, you’ll have to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 scroll up and down (using the vertical scroll bar) to view all the 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 material that pertains to the current question. 2 12345678901234567890123456789012123456789012345678901 R eading Com prehension: Passages are too long for you to see on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the screen in their entirety; you’ll need to scroll. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uantitative questions that include figures: Some figures— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 especially charts and graphs—won’t fit on the screen in their 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 entirety; you might need to scroll. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 01:06 Computer-Adaptive GMAT-Section 3:Quantitative 21 of 37 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test Section ? Answer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 21 Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard? 35 55 39 40 60

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Part I: Everything You Ever W anted to Know about the G M AT

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 01:09 Computer-Adaptive GMAT-Section 4:Verbal 6 of 41 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Questions 6 to 8 Beginning 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Test Section ? Answer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The CAT’s Word Processor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the two GM AT essay sections, you’ll use the simple word 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 processor built into the CAT system. While the word processor includes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some features standard in programs like Word and WordPerfect, it also 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 lacks many of these programs’ features. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Keyboard Commands for Navigation and Editing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere are the navigational and editing keys available in the CAT word 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 processor: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Backspace removes the character to the left of the cursor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Delete removes the character to the right of the cursor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Home moves the cursor to the beginning of the line. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • End moves the cursor to the end of the line. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Arrow Keys move the cursor up, down, left, or right. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Enter inserts a paragraph break (starts a new line). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Page Up moves the cursor up one page (screen). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Page Down moves the cursor down one page (screen). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 The Andean cordillera is made up of many interwoven mountain ranges, which include high intermountain plateaus, basins and valleys. The Northern Andes (5) contain several broad ecosystems falling into four altitudinal belts. Its northern subregion is distinguished from the rest of the region by higher relative humidity and greater climatic symmetry between the (10) eastern and western flanks of the range. The Central Andes are characterized by a succession of agricultural zones with varied climatic conditions along the mountains' flanks and by large, high(15) altitude plateaus, variously called puna or altiplano, which do not occur in the Northern Andes. The soil fertility of the northern altiplano is generally good. The western Central Andean ranges are (20) relatively arid with desert-like soils, whereas the eastern ranges are more humid and have more diverse soils. The eastern slopes of the Central Andes in many ways are similar to the wet forests

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In the passage, the author's primary concern is to describe the climate and topography of various regions of the Andean cordillera discuss the factors affecting the climate of the Andean cordillera suggest various alternative explanations for the diversity of climate among the various regions of the Andean cordillera examine the effects of topograpy on the climate and vegetation of the Andean cordillera compare and contrast the climate and topography of the Northern Andes to that the Central Andes

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Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Certain often-used features of standard word processing programs are not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 available in the CAT word processor. For example, no keyboard 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 commands are available for: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • TAB—disabled (does not function) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Beginning/end of paragraph (not available) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Beginning/end of document (not available) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N o key combinations (using the CTRL, ALT, or SH IFT key) or 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 other so-called “ macros” are available for editing functions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (You’ll use your mouse for cutting and pasting text.) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Mouse-Driven Navigation and Editing Functions 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Just as with other word processors, to navigate the editing screen you can 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 simply point the cursor to the position at which you wish to begin typing, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 then click. The CAT word processor also includes mouse-driven CUT, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PASTE, and UN DO . 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Selecting text you wish to cut. You select text the same way as with 2 12345678901234567890123456789012123456789012345678901 standard word processing programs: either (1) hold down your mouse 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 button while sweeping the I-beam on the screen over the desired text, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) hold down the SH IFT key and use the navigation keys to select text. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The CUT Button. If you wish to delete text but want to save it to a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 temporary clipboard for pasting elsewhere, select that text (see above) then 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 click on the CUT button. Cutting text is not the same as deleting it. When 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you delete text (using the DELETE key), you cannot paste it elsewhere in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your document (but see UN DO below). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The PASTE button. If you wish to move text from one position to another, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 select and cut the text, then reposition your cursor where you want the text 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to go and click on the PASTE button. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The UN DO button. Click on this button to undo the most recent delete, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cut, or paste that you performed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Limitations of CUT and UN DO. The following mouse-driven features are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not available: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • DRAG-AN D-DRO P cut-and-paste (not available) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • CO PY (not available; to copy you need to cut, then paste, in the 2 12345678901234567890123456789012123456789012345678901 same spot) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M ULTIPLE UN DO (the CAT word processor stores only your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m ost recent delete, cut, or paste, or keyboard entry.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 23

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The vertical scroll bar. O nce you key in ten lines or so, you’ll have to scroll 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to view your entire response. A vertical scroll bar also appears to the right 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the AWA prompt. Be sure to scroll all the way down to make sure you’ve 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 read the entire prompt. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Spell-checking, grammar-checking, fonts, attributes, hyphenation. The 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 CAT word processor does not include a spell-checker or grammar-checker, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nor does it allow you to choose typeface or point size. N either manual nor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 automatic hyphenation is available. Attributes such as bold, italics, and 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 underlining are not available. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 As for words that you would otherwise italicize or underline (such as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 titles or non-English words), it’s okay to leave them as is. The readers 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 understand the limitations of the CAT word processor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The GMAT CAT Test-Taking Experience 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When you take a test as important as the GM AT, it’s a good idea to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 minimize test anxiety by knowing exactly what to expect on exam 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 day—aside from the timed test itself. Let’s walk you through the various 2 2 12345678901234567890123456789012123456789012345678901 pre-test and post-test procedures and describe the physical testing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 environment. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 When You Arrive at the Test Center 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s what you can expect when you arrive at the test center: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The supervisor will show you a roster, which includes the names of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test-takers scheduled for that day, and will ask you to initial the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 roster next to your name, and indicate on the roster your arrival 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The supervisor will ask you to read a two-page list of testing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 procedures and rules. (I’ll cover all these rules in the pages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 immediately ahead.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The supervisor will give you a “ N ondisclosure Statement.” You’re 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to read the printed statement, then w rite the statement (in the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 space provided on the form) and sign it. In the statement, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 agree to the testing policies and rules, and you agree not to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 reproduce or disclose any of the actual test questions. The supervi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sor will not permit you to enter the exam room until you’ve 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 written and signed the statement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 24 123456789012345678901234567890121234567890123456789012

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • You’ll probably have to sit in a waiting room until the supervisor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calls your name. A 5- to 10-minute wait beyond your scheduled 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 testing time is not uncommon. (Taking the GM AT CAT is like 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 going to the dentist—in more than one respect!) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The supervisor will check your photo identification. (You won’t be 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 permitted to take the test unless you have one acceptable form of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 photo identification with you.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • The test center will provide a secure locker (free of charge) for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stowing your personal belongings during the test. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • To help ensure that nobody else takes any part of the exam in your 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 place, the supervisor will take a photograph of you. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The supervisor might give you some rudimentary tips about 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 managing your time during the exam. Just ignore the supervisor’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tips, because they might not be good advice for you! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Before you enter the testing room, you must remove everything 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from your pockets except your photo I.D. and locker key. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The supervisor will provide you with several pieces of scratch 2 12345678901234567890123456789012123456789012345678901 paper (stapled together), along with two pencils. These are the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only items you’ll have in hand as you enter the testing room. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Testing Procedures and Rules 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If you want to exit the testing room for any reason, you must raise 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 your hand and wait for the supervisor to come in and escort you from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the room. (You won’t be able to pause the testing clock for any 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 reason.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N o guests are allowed in the waiting room during your test. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N o food or drink is allowed in the testing room. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N o hats are allowed. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You must sign out whenever you exit the testing room. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You must sign in whenever you re-enter the testing room (the supervi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sor will ask to see your photo I.D. each time). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • If you need more scratch paper during the exam, just raise your hand 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and ask for it. The supervisor will happily replace your bundle with a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 fresh one. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The supervisor will replace your tired pencils with fresh, sharp ones 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 upon your request anytime during the exam (just raise your hand). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 25

Part I: Everything You Ever W anted to Know about the G M AT

www.petersons.com

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What You Should Know about the CAT Testing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Environment 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Individual testing stations are like library carrels; they’re separated by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 half-walls. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The height of your chair’s seat will be adjustable and the chair will 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 swivel. Chairs at most testing centers have arms. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Computer monitors are generally of the 15-inch variety. You can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adjust contrast. If you notice any flickering, ask the supervisor to 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 move you to another station. (You won’t be able to tell if you monitor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 has color capability, because the GM AT is strictly a black-and-white 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 affair.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can’t change the size of the font on the screen, unless you specifically 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 request before the exam begins that a special Z O O M TEXT function be 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 made available to you. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If your mouse has two buttons, you can use either button to click your 2 2 12345678901234567890123456789012123456789012345678901 way through the exam (both buttons serve the same function). Don’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expect that nifty wheel between buttons for easy scrolling, because 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you’re not going to get it. For all you gamers and laptop users, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trackballs are available, but only if you request one before you begin 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the test. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Testing rooms are not soundproof. During your test, you might hear 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 talking and other noise from outside the room. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Expect the supervisor to escort other test-takers in and out of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 room during your test. Do your best to ignore this potential distrac2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If the testing room is busy, expect to hear lots of mouse-clicking 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during your test. Because the room is otherwise fairly quiet, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incessant mouse-clicking can become annoying! 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Earplugs are available upon request. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Expect anything in terms of room temperature, so dress in layers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You’ll be under continual audio and video surveillance. To guard 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 against cheating, and to record any irregularities or problems in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 testing room as they occur, the room is continually audiotaped and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 videotaped. (Look for the cameras or two-way mirrors, then smile and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wave!) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

N ote

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Before You Begin the Test—The Computer Tutorial 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O kay, the supervisor has just escorted you into the inner sanctum and to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your station, and has wished you luck. (Some supervisors have been 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 known to encourage test-takers to “ have fun!” ) Before you begin the test, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the CAT System will lead you through a tutorial which includes five 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sections (each section steps you through a series of “ screens” ): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. H ow to use the mouse (6 screens) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2. H ow to select and change an answer (6 screens) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. H ow to scroll the screen display up and down (6 screens) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4. H ow to use the toolbars (21 screens); here you’ll learn how to: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Q uit the test. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Exit the current section. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Access the directions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Confirm your response and move to the next question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. H ow to use the AWA word processor features (14 screens) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you want to see what some of the tutorial screens look like, ETS 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provides a variety of samples in its official GM AT Bulletin. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s what you need to know about the CAT tutorial: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You won’t be able to skip any section or any screen during 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the tutorial. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • As you progress, the system requires that you demonstrate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 competency in using the mouse, selecting and confirming answer 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 choices, and accessing the directions. So you can’t begin taking the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 actual test unless you’ve shown that you know how to use the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 system. (Don’t worry: no test-taker has ever flunked the CAT 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 system competency test.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • At the end of each tutorial section (series of screens), you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 repeat that section, at your option. But once you leave a section 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you can’t return to it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 27

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Don’t choose to repeat any tutorial section. Why not? If you do, you’ll be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forced to step through the entire sequence of screens in that section again 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (an aggravating time-waster, especially for the 21-screen section!) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The AWA section of the tutorial allows you to practice using the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 word processor. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If you carefully read all the information presented to you, expect 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to spend about 20 minutes on the tutorial. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n test day, you’ll already know how the CAT system works. So step 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 through the tutorial as quickly as you can, reading as little as possible. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can easily dispense with the tutorial in 5–10 minutes this way. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Remember: The less time you spend with the tutorial, the less fatigued 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll be during the exam itself. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Post-Test GMAT CAT Procedures 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O kay, it’s been about 4 hours since you first entered the testing center, and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ve just completed the second of two multiple-choice GM AT sections. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You may think you’ve finished the CAT, but the CAT has not quite finished 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with you yet! There are a few more hoops to jump through before you’re 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 done. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Respond to a brief questionnaire. The CAT will impose on you a brief 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questionnaire (presented in a series of screens) about your test-taking 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 experience (believe it or not, these questions are multiple-choice, just 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 like the exam itself). The questionnaire might ask you, for example: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Whether your supervisor was knowledgeable and helpful 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Whether the testing environment was comfortable 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • H ow long you waited after you arrived at the testing site to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 begin the test 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Whether you were distracted by noise during your exam 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Cancel your test, at your option. The most important question you’ll 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 answer while seated at your testing station is this next one. The CAT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will ask you to choose whether to: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Cancel your scores (no scores are recorded; partial cancellation 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is not provided for) or see your scores immediately. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Tip

Alert!

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O nce you elect to see your scores, you can no longer cancel them—ever! So 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you should take a few minutes to think it over. The CAT gives you 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 minutes to choose. If you haven’t decided within 5 minutes, the CAT will 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 automatically show you your scores (and you forfeit your option to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cancel). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you click on the CAN CEL SCO RES button, the CAT will then give you 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 yet another 5 minutes to think over your decision. So you really have 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 minutes altogether to make up your mind. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. View and record your scores. If you elect to see your scores, you 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 should write them down on your scratch paper. When you leave the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 testing room, the supervisor will allow you to transcribe them onto 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 another sheet of paper (one that you can take home with you), so that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you don’t have to memorize them. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Direct your scores to the schools of your choice. O nce you’ve elected 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to see your scores, the CAT will ask you to select the schools you wish 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to receive your score report (the CAT provides a complete list of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 schools). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can select as many as five schools at this time—without incurring an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional fee. This is your last chance for a freebie, so you should take 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 full advantage of it. Be sure to compile your list of five schools before 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Before You Leave the Testing Center 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Upon exiting the testing room for the final time, the following will happen: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The supervisor will collect your pencils and scratch paper, and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 will count the number of sheets of paper to make sure you aren’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trying to sneak out with any. (Then, if you’re lucky, you’ll be 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 allowed to watch while the supervisor ceremoniously rips up your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scratch paper and drops it in the trash basket!) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The supervisor will remind you to collect your belongings from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your locker (if you used one), and turn in your locker key. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. The supervisor will provide you with an ETS pamphlet that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explains how to interpret your test scores. (You can take this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 home with you.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 29

Part I: Everything You Ever W anted to Know about the G M AT

Alert!

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The supervisor might also provide you with a postcard-sized invitation to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ blow the whistle” on anybody you suspect of cheating on the exam (the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 invitation ends with the assurance: “ Confidentiality guaranteed” ). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2345678901234567890123456789012123456789012345678901 2 1 Top 10 Tips for GMAT Prep 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Regardless of what books, software, or other GM AT-prep resources you’re 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 using, certain time-tested strategies for GM AT prep never go out of style. To 2 2 12345678901234567890123456789012123456789012345678901 attain your optimal GM AT score, and to maximize your chances of getting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 into your first-choice B-school, heed the following points of sage advice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Don’t Neglect Your Weaknesses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In gearing up for the GM AT, many test-takers make the mistake of focusing 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on their strengths while neglecting their weaknesses. They tell themselves: 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ I can’t handle this tough stuff right now; so I’ll either face it later or skip 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 it altogether and hope to make some lucky guesses on the exam.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But, you can’t hide any of your individual GM AT scores from B-school 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 admissions officers. So, don’t spin your GM AT-prep wheels by spending 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more time than you need on any one area of the GM AT, or by rehashing 2 2 12345678901234567890123456789012123456789012345678901 what you already know. Devote more time to improving on your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weaknesses than basking in your strengths. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Don’t Neglect the Two GMAT Essay Sections 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT “ prep neglect” is especially commonplace when it comes to the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two GM AT essay sections—a bit ironic, considering that it’s impossible to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 guess, or “ fake,” your way through an essay. What’s more, the B-schools 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are focusing more and more on the GM AT essays to help them make tough 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decisions among applicants—many of whom appear equally qualified 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 otherwise. So, your AWA score might very well make the difference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between acceptance and rejection, especially for a B-school where you’re a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 borderline candidate. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Fast, accurate typists have a clear advantage when it comes to the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT essay sections—no doubt about it. So if you’re a poor typist, work 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on improving your speed and skill before exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 30 123456789012345678901234567890121234567890123456789012

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Practice under Exam Conditions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When it comes to GM AT prep, there’s simply no substitute for “ putting 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself to the test” by taking practice questions under simulated testing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conditions. H ere are some suggestions: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 • Adhere to the time limits that each exam section imposes. 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • If possible, use a word processor for composing your practice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essays; use only the features available on the CAT word processor. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • If possible, take at least one computer-based practice test. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Also, do not underestimate the role that endurance plays on the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 GM AT. H alf the battle is just making it through the half-day ordeal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with your wits intact. Condition yourself by taking at least one full2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 length practice test straight through, with only a few short breaks. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Take the Real GMAT Once—Just for Practice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you have time and can afford it, you should register for and take the real 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 GM AT once as a dress rehearsal—just to get comfortable with the testing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 environment. You’ll rid yourself of a lot of anxiety and nervousness and, if 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re like most test-takers, you’ll be far more relaxed and focused the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 second time around. In fact, ETS statistics show that among repeaters, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 more than 90% improve their score the second time around. Those are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 great odds! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. Keep Practice Scores in Perspective 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you’re like most GM AT test-takers, you’ve set your sights on two or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three particular colleges or universities as your top choices, and you have a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 good idea what GM AT scores you’ll need for getting into those schools. So 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perhaps you’ve set a goal for your GM AT scores. That’s understandable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 But don’t psyche yourself out by obsessing over your practice-test scores. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Gloating over high scores can lead to complacency and overconfidence, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 while brooding over low scores can result in discouragement and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 self-doubt. Either way, you’re sabotaging yourself. The bottom line: Try to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concern yourself not with test scores themselves but rather with what you 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 can constructively do between now and exam day to improve these scores. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. Maintain the Right “GMATitude” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 It’s important to maintain a positive attitude about the GM AT. But, it’s 2 12345678901234567890123456789012123456789012345678901 also important to keep your self-confidence from swelling to the point of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 complacency and overconfidence. Think you can just “ wing it” on the 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 31

Part I: Everything You Ever W anted to Know about the G M AT

32

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GM AT and still crush the competition? Think again. Even if you were a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 curve-raiser in college, there are thousands of others like you who are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 taking the GM AT very seriously and who would be more than happy to 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 bump you down the GM AT-scoring curve. Enough said? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 7. Be Realistic in Your Expectations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’d love perfect GM AT scores, wouldn’t you? And in theory, your 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 capable of attaining them. But in reality, you probably won’t score as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 highly as you’d like to. Accept your limitations. With regular study and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 practice, you’ll perform as well as you can reasonably expect to perform. 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Also be realistic about the benefits you expect from this or any other 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 GM AT preparation book. There’s only so much that you can do in a few 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weeks—or even several months—to boost your GM AT score. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8. Take Steps to Minimize GMAT Anxiety 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test anxiety, whether before or during a test, can only hinder your 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 performance. Although it’s a good idea to try to keep a lid on it, don’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expect to eliminate it entirely. If you’re starting to feel the heat, try the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 following anxiety-busting techniques. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Practice testing under exam conditions is the best method of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reducing test anxiety. As you become more comfortable in a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 simulated testing environment, your nerves will begin to settle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 down, and the real test will seem more like “ just another day at 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the office.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Join (or form) a GM AT study group. O penly discuss your insecuri2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ties about the GM AT, and you’ll notice that they begin to dissipate. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Before taking practice tests, try simple relaxation techniques such 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as stretching, quieting your thoughts, deep breathing, or whatever 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 else works for you. Some people find a quick burst of vigorous 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exercise to be highly effective. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You’ll be anxious about the GM AT only if you’re actually thinking 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about it. So during the weeks that you’re gearing up for the test, 12345678901234567890123456789012123456789012345678901 2 keep yourself preoccupied with your everyday activities. Try not to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discuss the GM AT with others except during planned study 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sessions or classes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 9. Know When You’ve Peaked 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Preparing for the GM AT is a bit like training for an athletic event. You 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to familiarize yourself with the event, learn to be comfortable with 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 it, and build up your skill and endurance. At some point—hopefully 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 around exam day—your motivation, interest, and performance will 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 peak. Sure, it takes som e time and effort to get comfortable with the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 exam, to correct poor test-taking habits, to bone up on whatever math 2 2 12345678901234567890123456789012123456789012345678901 and grammar you might have forgotten, to develop an instinct for 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 recognizing wrong-answer choices, and to find your optimal pace. But 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 there’s a point beyond which additional study and practice confer little 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or no additional benefit. Don’t drag out the process by starting several 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 months in advance or by postponing the GM AT to give yourself more 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time than you really need for preparation. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10. Take the GMAT Early to Allow Yourself the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Option of Retaking It 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 M ost graduate business schools admit new students for the fall term only. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Although application deadlines vary widely among schools, if you take the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT no later than the N ovember prior to matriculation, you’ll meet 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 almost any application deadline. Ideally, you should take the GM AT early 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 enough so that you can take the exam a second time if necessary and still 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 meet application deadlines. In any event, schedule the GM AT so that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re sure you will have adequate time to prepare beforehand. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Top 10 GMAT Test-Taking Tips 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Parts II–IV, you’ll learn strategies and tips for specific test sections and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question types. Right now, however, review some general strategies for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the GM AT. Even if you’ve read about these strategies elsewhere, of if 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 they seem like common sense to you, it’s a good idea to reinforce them in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your mind. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Know Your Optimal Pace, and Stay on It 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Time is definitely a factor on every section of the GM AT. O n the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 multiple-choice sections, expect to work at quicker pace than is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 comfortable for you. Similarly, the 30-minute time limit for each AWA 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 response requires a lively writing pace, allowing little time for editing, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 revising, and fine-tuning. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the multiple-choice sections, check your pace after every 10 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 questions or so (three times during a section), and adjust it accordingly so 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 33

Part I: Everything You Ever W anted to Know about the G M AT

34

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that you have time to at least consider every question in the section. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During each essay section be sure to leave yourself enough time to cover all 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your main points and to wrap up your essay with a brief concluding 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 paragraph. The best way to avoid the time squeeze is to practice under 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 timed conditions, so that you get a sense for your optimal pace. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. If You’re Not Sure What the Correct Answer Is, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Don’t Dwell on It . . . Move on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This tip is closely related to the previous one. You might find yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reluctant to leave a question until you’re sure your answer is correct. The 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 design of the CAT contributes to this mind set, because your reward for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct responses to difficult questions is greater than your reward for 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 easier questions. But a stubborn attitude will only defeat you, because it 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reduces the number of questions you may attempt, which in turn can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lower your score. Set aside your perfectionist tendencies and remember: 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 You can miss quite a few questions and still score high. Develop a sense 2 2 12345678901234567890123456789012123456789012345678901 of your optimal pace—one that results in the greatest number of correct 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 responses. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Take Your Time with the First Few Quantitative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and Verbal Questions 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The CAT uses your responses to the first few questions to move you either 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 up or down the ladder of difficulty. O f course, you want to move up the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ladder, not down. So take great care with the initial questions—perhaps 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 moving at a somewhat slower pace. O therwise, you’ll have to answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 several questions just to reverse the trend by proving to the CAT that 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you’re smarter than it thinks you are. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Avoid Random Guesswork, If Possible 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you must guess, always try to eliminate obvious wrong-answer choices 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first, then go with your hunch. Eliminating even one choice improves your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 odds. If you’re out of time on a section, there’s no advantage to guessing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 randomly on the remaining questions. Why? You might luck out and guess 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correctly. H owever, incorrect responses move you down the ladder of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficulty, and correct responses to easier questions aren’t worth as much 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as correct responses to more difficult questions. So on balance, there’s no 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 net advantage to guessing randomly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. Read Each Question in Its Entirety, and Read 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Every Answer Choice 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll discover in the days ahead that the test-makers love to bait you with 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tempting wrong-answer choices. This applies to every type of multiple2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice question on the exam. So unless you’re quickly running out of time, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 never confirm an answer until you’ve read all the choices! This blunder is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one of the leading causes of incorrect responses on the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. Maintain an Active Mind Set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the GM AT, it’s remarkably easy to fall into a passive mode—one in 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 which you let your eyes simply pass over the words while you hope that the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct response jumps out at you as you scan the answer choices. Fight 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 this tendency by interacting with the test as you read it. Keep in mind that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each question on the GM AT is designed to measure a specific ability or 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 skill. So try to adopt an active, investigative approach to each question, in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which you ask yourself: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • What skill is the question measuring? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • What is the most direct thought process to determine the correct 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 response? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • H ow might a careless test-taker be tripped up on this type of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answering these three questions is, in large part, what the rest of this book 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is all about. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7. Use Your Pencil and Scratch Paper 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Using pencil and paper helps keep you in an active mode. M aking brief 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 notes and drawing diagrams and flow charts will help keep your thought 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 process clear. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8. Move the Keyboard Aside for the Multiple-Choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sections 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You won’t use the keyboard at all for these sections. So put your scratch 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 paper right in front of you, and get the keyboard out of the way. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 35

Part I: Everything You Ever W anted to Know about the G M AT

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9. Know the Test Directions Inside and Out—Before 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You Take the Test 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Just before the first question of each type (e.g., Data Sufficiency or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Reading Comprehension) the CAT will display the directions for that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question type. The clock will be running, so dismiss the directions as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 quickly as possible by clicking on the DISM ISS DIRECTIO N S button. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 time to read (This advice presupposes that you already know the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 directions—which of course you will!) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10. Use the 5-Minute Breaks, but Keep an Eye on 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the Time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Remember: The GM AT CAT clock is always running, even during the two 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scheduled 5-minute breaks. By all means, take advantage of these breaks 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to leave the room, perhaps grab a quick snack from your locker, and do 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some stretching or relaxing. But don’t get too relaxed! Five minutes goes 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by very quickly, and the test will begin after that time has elapsed—with or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without you! 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Resources for GMAT Preparation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow much should you “ invest” in your GM AT education—in terms of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both time and money? The conventional wisdom is that since the GM AT is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 one of the most important tests you’ll ever take, you should invest as much 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 time and money in it as possible. H owever, the law of diminishing returns 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 applies to GM AT preparation. This book, along with a few other 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 thoughtfully selected resources, can provide virtually all of the potential 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 benefits of a full-blown GM AT prep course. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GMAT Books 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The number of available books for GM AT prep is overwhelming. H ere are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some suggestions to help you cut through the glut: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Peruse a book carefully before committing to it. Yes, this means 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 visiting your local brick-and-mortar bookstore. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Look for a book that emphasizes skill development, not just 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 practice questions. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Rule out any book that emphasizes so-called “ secrets” and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ shortcuts,” or makes the test out to be easier than it appears. Do 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you really think the GM AC and ETS would devise a test that can 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 be “ cracked” like a cheap safe? If so, think again. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 36 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 1: The GM AT—In a N utshell

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Limit the number of comprehensive GM AT books you use to two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or three altogether. Any more any you’ll find yourself reading the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same strategies and test-taking tips again. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Identify your weakest skill area, and supplement this book with a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 workbook targeted at that area. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 If you must shop for GM AT books at an online bookstore, ignore 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 customer comments and ratings, especially if they are few in number. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Laudatory comments are often submitted anonymously by the publishers 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 themselves, while derogatory comments are often factually inaccurate, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unfair, and inflammatory. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The bottom line: You don’t need to spend more than $40 to $50, on three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or four books altogether, to be fully prepared for the GM AT. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Online GMAT Resources 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Web is now littered with GM AT advice and practice questions—freely 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 available for public consumption. To separate the wheat from the chaff, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 limit your GM AT web-surfing to the official GM AC site (www.mba.com) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and the sites of test-prep publishers with a time-tested reputation for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 producing high-quality content, such as Peterson’s (www.petersons.com). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GMAT-Prep Courses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Would it be worthwhile to enroll in a live GM AT-prep course? Well, here 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are the advantages: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The dynamics of a live classroom setting can help you learn 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 difficult concepts by affording different perspectives. (But why 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 not start your own study group? You’re just as likely to gain 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 useful insights from your peers as from a GM AT instructor.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. H aving made a substantial financial investment, you’ll probably 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 be motivated to get your money’s worth out of that investment. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (But this is an expensive head game, isn’t it? And if you can’t 2 12345678901234567890123456789012123456789012345678901 afford the course, it doesn’t matter anyway.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. You’re less likely to procrastinate with a set class schedule. (But if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re disciplined enough this is no advantage.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. All the materials are provided, so you don’t need to decide which 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 books and/or software to buy. (But is this really a significant 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 benefit?) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 37

Part I: Everything You Ever W anted to Know about the G M AT

38

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. You can commiserate and compare notes with your classmates. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fact, GM AT prep classes typical morph into de facto pre-M BA 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 support groups. (But why not start your own GM AT study/ 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 support group?) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are some drawbacks and caveats to keep in mind if you’re thinking 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 about taking a GM AT prep-course: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. They’re expensive; you can easily spend $1,000. (If you’re near a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 university, you might find a course sponsored by the university, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 perhaps through its extension program, for a fraction of the cost 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of a private course.) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. Despite their claims, private test-prep companies pass along no 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ secrets” to you—nothing at all that you can’t find for yourself in 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test-prep books. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. The popular test-prep services require each of their GM AT 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 instructors to have taken the real GM AT and attained a high 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 score (typically above the 90th percentile). But this screen hardly 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ensures that your instructor will be an effective teacher. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. During peak times of the year, you might have difficulty 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 scheduling out-of-class time in the computer lab, at least during 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 reasonable hours. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. If you’re not located in a major urban area or near a large college 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or university, the class location might be too remote for you. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you decide to enroll in a GM AT prep-course, keep in mind the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points of advice: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Ask about the policy for repeating the course. Insist on an option 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to repeat the course at least once without charge at any time (not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just within the next year). 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Ask about merit-based or financial-based “ scholarships” (fee 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reductions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. If you repeat the course, be sure to arrange for a different 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 instructor; just as with GM AT books, each GM AT instructor has 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 his or her own teaching style. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. The most significant benefit of a GM AT course is the live 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 classroom; so be sure to attend as many classes as you can. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. Take full advantage of the chance to meet other students and set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 up out-of-class study sessions. As we’ve already noted, you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 learn just as much from your peers as from an instructor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 1: The GM AT—In a N utshell

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GMAT Availability and Registration 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The computer-based GM AT is administered year-round at more than 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 500 locations, most of which are in N orth America. Testing centers are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 located at Prometric Testing Centers, Sylvan Learning Centers, certain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 colleges and universities, and ETS (Educational Testing Service) field 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 offices. The official GM AT Bulletin contains a complete list of GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 computer-based test centers; an updated list is available at the GM AC 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Web site (www.mba.com). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Registering for the GMAT 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 To take the computer-based GM AT, you must schedule an appointment by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using any of the following four methods: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. M ake an appointment online, via the GM AC Web site 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (www.mba.com). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Call the test center of your choice directly. A current test center 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 list is available at the GM AC Web site (www.mba.com). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Call a central registration number: 1-800-GM AT-N O W (1-8002 12345678901234567890123456789012123456789012345678901 462-8669). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. M ake an appointment by mail. (You’ll need to complete and mail 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the Authorization Voucher Request Form in the official GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Bulletin; you should receive your Authorization Voucher about 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 four weeks after you mail the request form, and you cannot 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 schedule a test appointment until you’ve received your voucher.) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You might be able to sit for the GM AT within a few days after scheduling 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an appointment. H owever, keep in mind that popular test centers may 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 experience backlogs of up to several weeks. Also, you might find it more 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 difficult to schedule a weekend test date than a weekday test date. So be 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sure to plan ahead and schedule your GM AT early enough to meet your 2 12345678901234567890123456789012123456789012345678901 B-school application deadlines. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In certain areas outside of N orth America, the computer-based network is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not yet available, and the GM AT is still administered as a paper-based 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 exam. A complete list of international paper-based testing locations and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test dates is available at the GM AC Web site (www.mba.com). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Obtaining Up-to-Date GMAT Information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For detailed information about GM AT registration procedures, consult 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the official GM AC Web site (www.mba.com), or refer to the printed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 GM AT Bulletin, published annually by the GM AC. This free bulletin is 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 39

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 available directly from ETS and GM AC, as well as through career- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 planning offices at most four-year colleges and universities. You can also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 download the Bulletin from the GM AC Web site. The official GM AC Web 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 site and Bulletin both provide detailed and current information about: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Test center locations, telephone numbers, and hours of operation 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Registration procedures 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Accommodations for disabled test-takers 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Requirements for admission to the GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Registration and reporting fees, and refund policies 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Repeating the test 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The paper-based GM AT (availability, registration procedures, etc.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O fficial scoring criteria for the AWA essays 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • H ow GM AT scores should be used by the institutions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GM AT Bulletin is published only once a year, so for the most 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 up-to-date official information you should check the GM AC Web site. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Contacting the Testing Service 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To obtain the Bulletin, or for other information about the GM AT, you can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contact ETS using any of the following methods: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Telephone: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1-609-771-7330 (general inquiries and publications) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1-800-462-8669 (CAT registration only) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E-mail: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 [email protected] 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 World Wide Web: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 www.mba.com 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 www.ets.org (the ETS home page) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Mail: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Educational Testing Service 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 P.O . Box 6103 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Princeton, N J 08541-6103 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter

2

N ote

The GMAT—Up Close 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Chapter 1, you learned that the GM AT consists of three parts and that 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test questions come in seven different formats. H ere’s a recap: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test Section Question Formats 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analytical Writing Assessment Analysis of an Issue 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Sections 1 and 2) Analysis of an Argument 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uantitative Ability Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Section 3) Data Sufficiency 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Verbal Ability Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Section 4) Sentence Correction 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this chapter, you’ll examine each format in detail. Specifically, you’ll: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn what abilities and content areas the format covers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Examine the test directions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Look at one or two example questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Review the format’s key features 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For each multiple-choice format, you’ll look at two questions—one a bit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 easier than average, the other a bit tougher than average—along with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explanatory answers. You can use these sample questions to help 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 determine if you should Tak e It to the N ex t L evel. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 41

Part I: Everything You Ever W anted to Know about the G M AT

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Analytical Writing Assessment (AWA) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Chapter 1, you learned that the GM AT Analytical Writing Assessment 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 consists of two separate timed sections: (1) Analysis of an Issue and (2) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis of an Argument. These two sections have a lot in common. For 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each section: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • You compose an essay response using the test’s built-in word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 processor. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Your time limit is 30 minutes. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Your essay topic, or “ prompt,” is drawn randomly from a large 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 pool. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Your essay will be evaluated based on four broad areas: (1) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 content, (2) organization, (3) writing style, and (4) mechanics 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (grammar, syntax, word usage, etc.). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere, you’ll take a closer look at each of the two AWA sections. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Analysis of an Issue (1 Writing Task, 30 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the Issue-Analysis section, your task is to compose an essay in 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which you respond to a brief (1–2 sentence) opinion about an issue of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 general intellectual interest. You should consider various perspectives, take 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a position on the issue, and argue that position. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Issue-Analysis section is designed to test your ability to present a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 position on an issue effectively and persuasively. In scoring your Issue 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay, readers will consider how effectively you do the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognize and deal with the complexities and implications of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 issue. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O rganize, develop, and express your ideas. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Support your ideas (with reasons and examples). 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Control the elements of Standard Written English. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 During the pre-test tutorial, as well as at the start of your timed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue-Analysis section, the GM AT will present to you one screen providing 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 directions and guidelines specific to the Issue-Analysis writing task. The 2 2 12345678901234567890123456789012123456789012345678901 screen will describe the task generally, and indicate the four general 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scoring criteria. H ere’s essentially what you’ll see on this screen: 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 42 123456789012345678901234567890121234567890123456789012

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Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 This writing task is designed to test your ability to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 present a position on an issue effectively and per12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 suasively. Your task is to analyze the issue pre2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sented, considering various perspectives, and to de2 12345678901234567890123456789012123456789012345678901 2 velop your own position on the issue. In scoring 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 your Issue essay, readers will consider how effec2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tively you: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Recognize and deal with the complexities and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 implications of the issue. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • O rganize, develop, and express your ideas. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Support your ideas (with reasons and examples). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Control the elements of Standard Written 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 English. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The screen will also indicate rules and guidelines for the Issue writing task. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s essentially what you’ll see further down the screen: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Your time limit is 30 minutes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Writing on any topic other than the one pre2 12345678901234567890123456789012123456789012345678901 sented is unacceptable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The topic will appear as a brief statement on an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 issue of general interest. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You are free to accept, reject, or qualify the state2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You should support your perspective with rea2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sons and/or examples from such sources as your 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 experience, observation, reading, and academic 2 12345678901234567890123456789012123456789012345678901 2 studies. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You should take a few minutes to plan your re2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sponse before you begin typing. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You should leave time to reread your response 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and make any revisions you think are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 43

Part I: Everything You Ever W anted to Know about the G M AT

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44

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can access the directions and guidelines at any time during the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Issue-Analysis section by clicking on the H ELP button. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 What Issue-Analysis Questions Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each Issue-Analysis topic in the official pool consists of a statement of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 opinion, which appears in quotes, followed by a brief directive (statement 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of your task). H ere’s an example, which is similar to some of the topics in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the official pool—although you won’t see this one on your exam (the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 directive follows the quoted statement): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ People often complain that the introduction of new labor-saving 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 machines costs workers their jobs. H owever, most new technologies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 create more jobs than they destroy.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Discuss the extent to which you agree or disagree with the foregoing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement. Support your perspective using reasons and/or examples 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 from your experience, observation, reading, or academic studies. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although each statement in the official GM AT pool is distinct, many of them 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 cover similar thematic ground. H ere are the different themes to look for 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (understandably, more topics involve business issues than any other type): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Business—organizational structure/behavior, management 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Culture and social mores, attitudes, values 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Business productivity, efficiency, and teamwork 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Business—labor and employment issues 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 • Education—its overall role and objectives 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Government’s role in ensuring the welfare of its citizens 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Technology and its impact on business and society 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Keys to individual success 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Business—its overall role and objectives in society 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Business ethics 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Personal qualities and values 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Government’s role in regulating business, commerce, speech 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • “ Global village” issues 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Bureaucracy and “ the system” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Business—advertising and marketing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learning lessons from history 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Individual power and influence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 These categories are not mutually exclusive; in other words, many Issues 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 could fall into more than one category. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Issue Analysis 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 H ere are some key facts about the Issue-Analysis section (most of these are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 review): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The CAT will select your topic randomly from a large pool. You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t be able to choose among topics. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • All directives in the official pool are not identical. Your directive 2 12345678901234567890123456789012123456789012345678901 2 might differ slightly from the one in the preceding example. For 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example, your directive might ask you: “ In your opinion, how 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 accurate is the foregoing statement?” Regardless of how the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 directive is framed, however, you essential task is always the same: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 adopt a position on the issue, then support it with sound reasons 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and relevant examples. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • There is no “correct” answer. What’s important is how effectively 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you present and support your position, not what your position is. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The Issue-Analysis section is not intended to test your technical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 knowledge of any topic. O f course, you’ll need some familiarity 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 with the topic at hand. But, don’t worry if you’re no expert on the 2 12345678901234567890123456789012123456789012345678901 2 subject. The test-makers are far more interested in your ability to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assemble a well-organized, cohesive essay under time pressure than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in your knowledge of any specific subject. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • GMAT readers appreciate your time constraint and focus less on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 minutia than on the big picture. In evaluating and scoring your 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 essay, the readers will focus primarily on substance and organiza2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion. You writing “ style” and your mechanics (grammar, syntax, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 word usage, etc.) are secondary factors, which will come into play 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only if problems in these areas interfere with the reader’s under12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 standing of the ideas you’re intending to convey in your essay. You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t be penalized for errors in spelling and punctuation—unless 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these errors are frequent and egregious. (The CAT word processor 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 does not include a grammar- or spell-checker.) 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 45

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Analysis of an Argument (1 Writing Task, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 30 Minutes) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the Argument-Analysis section, your task is to compose an essay in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which you critique a paragraph-length argument based on the strength of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the evidence presented in support of it and on the argument’s logic (line of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 reasoning). You can also indicate what additional evidence would help you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evaluate the argument, and how the argument could be improved. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Argument-Analysis section is designed to test your critical-reasoning 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 and analytical-writing skills. In scoring your Argument essay, the reader 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will consider how effectively you: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Identify and analyze the key elements of the argument. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O rganize, develop, and express your critique. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Support your ideas (with reasons and examples). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Control the elements of Standard Written English. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During the pre-test tutorial, as well as at the start of your timed 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Issue-Analysis section, the GM AT will present two screens of directions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and guidelines specific to the Argument-Analysis writing task. The first 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 screen will describe the task generally and indicate the four general scoring 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 criteria. H ere’s essentially what you’ll see on the first screen: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 This writing task is designed to test your critical2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning skills as well as your writing skills. Your 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 task is to critique the stated argument in terms of its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 logical soundness and in terms of the strength of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the evidence offered in support of the argument. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scoring your Argument essay, the reader will con12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sider how effectively you: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Identify and analyze the key elements of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 argument. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O rganize, develop, and express your critique. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Support your ideas (with reasons and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Control the elements of Standard Written 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 English. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

N ote

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The screen will then indicate additional rules and guidelines. H ere’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essentially what you’ll see farther down the screen: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Your time limit is 30 minutes. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You must critique the logical soundness of the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 argument presented. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A critique of any other argument is unacceptable. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • You should take a few minutes to plan your re2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sponse before you begin typing. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • You should develop your ideas fully and organize 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them in a coherent manner. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You should leave time to reread your response 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and make any revisions you think are needed. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The second screen will indicate specific guidelines for critiquing the 2 12345678901234567890123456789012123456789012345678901 Argument. H ere’s essentially what you’ll see on the second screen: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You are not being asked to agree or disagree with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any of the statements in the argument. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You should analyze the argument’s line of rea2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 soning. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You should consider questionable assumptions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 underlying the argument. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You should consider the extent to which the evi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dence presented supports the argument’s conclu12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sion. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You may discuss what additional evidence would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 help strengthen or refute the argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You may discuss what additional information, if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any, would help you to evaluate the argument’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can access the two screens of directions and guidelines at any time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during the Argument-Analysis section by clicking on the H ELP button. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 47

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What Argument-Analysis Questions Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Argument on your exam will be drawn randomly from a large pool. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each Argument in the official pool consists of a paragraph-length passage, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 which presents the argum ent itself, followed by a directive (statement of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your task). The directive is the same for every Argument in the official 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pool. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Argument will appear as a quotation from a specified fictitious source. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s an example similar to the ones in the official pool—although you 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 won’t see this one on your exam (the directive follows the Argument): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The following recommendation appeared in a memo from the 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 H illsville City Council to the city’s mayor: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The private firm Trashco provides refuse pickup and disposal as well 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as recycling services for the town of Plattsburg. Trashco’s total fees for 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 these services are about two thirds what H illsville pays Ridco for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same services. In order to save enough money to construct a refuse 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 transfer station within our city limits, H illsville should discontinue 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using Ridco’s services and use Trashco’s services instead.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Discuss how well reasoned you find this argument. In your discussion, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 be sure to analyze the line of reasoning and the use of evidence in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument. For example, you may need to consider what questionable 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 assumptions underlie the thinking and what alternative explanations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or counterexamples might weaken the conclusion. You can also 2 2 12345678901234567890123456789012123456789012345678901 discuss what sort of evidence would strengthen or refute the argument, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what changes in the argument would make it more logically sound, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and what, if anything, would help you to better evaluate its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Argument Analysis 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere are some key facts about the Argument-Analysis section (most are 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 review): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The CAT will randomly select your Argument-Analysis prompt 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from a large pool. As in the Issue-Analysis section, you won’t be 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 able to choose among topics. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • All Arguments in the official pool contain the same directive. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Learn the directive that follows the quoted Argument before the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 exam, and you won’t need to read it during the exam. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The Argument-Analysis task is much different than the Issue2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis task. There’s no “ correct’ answer to any Issue-Analysis 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 question. But, when it comes to the Argument-Analysis task, it’s a 2 12345678901234567890123456789012123456789012345678901 2 1 different story. The argument that you critique will contain at least 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 three major problems in the use of evidence, reasoning, and logic; 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to score high on your Argument-Analysis essay, you must identify 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and discuss each major problem. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • You don’t need technical knowledge or special training in logic to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 score high. GM AT arguments are designed so that you can analyze 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 them by applying general reasoning skills and common sense. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • GMAT readers appreciate your time constraint and focus less on 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 minutia than on the big picture. Just as with the Issue-Analysis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 section, the readers will focus primarily on substance and organi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 zation. You writing “ style” and your mechanics (grammar, syntax, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 word usage, etc.) are secondary factors, and you won’t be penal2 12345678901234567890123456789012123456789012345678901 ized for errors in spelling and punctuation unless these errors are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 frequent and egregious. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Quantitative Ability Section 2 12345678901234567890123456789012123456789012345678901 2 1 (37 Questions, 75 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Before examining the two question formats—Problem Solving and Data 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Sufficiency—that the test-makers use for Q uantitative Ability questions, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 let’s first cover what’s common to both formats. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Both types of questions—Problem Solving and Data Sufficiency—are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 designed to measure the following general skills: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your proficiency in arithmetical operations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your proficiency at solving algebraic equations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your ability to convert verbal information to mathematical terms 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Your ability to visualize geometric shapes and numerical relation12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ships 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your ability to devise intuitive and unconventional solutions to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conventional mathematical problems 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a breakdown of the specific areas covered on the Q uantitative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 section, along with their frequency of appearance: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Properties of N umbers and Arithmetical O perations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (13–17 Q uestions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Linear ordering (positive and negative numbers, absolute value) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Properties of integers (factors, multiples, prime numbers) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Arithmetical operations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 • Laws of arithmetic 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 49

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Fractions, decimals, and percentages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Ratio and proportion 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Exponents (powers) and roots 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Average (arithmetic mean), mode, and median 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Basic probability 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Algebraic Equations and Inequalities (11–15 Q uestions) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Simplifying linear and quadratic algebraic expressions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Solving equations with one variable (unknown) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Solving equations with two variables (unknowns) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Solving factorable quadratic equations 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Inequalities 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Geometry, Including Coordinate Geometry (5–8 Q uestions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Intersecting lines and angles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Perpendicular and parallel lines 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Triangles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Q uadrilaterals (4-sided polygons) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Circles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Rectangular solids (three-dimensional figures) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Cylinders 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Pyramids 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Coordinate geometry 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Interpreting Statistical Charts, Graphs, and Tables (2–4 Q uestions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Pie charts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Tables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Bar graphs 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Line charts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Algebraic concepts on the GM AT are those normally covered in a 2 2 12345678901234567890123456789012123456789012345678901 first-year high school algebra course. The Q uantitative Ability section 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 does N O T cover these skills and math areas: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Complex calculations involving large and/or unwieldy numbers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Advanced algebra concepts 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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N ote

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Formal geometry proofs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Trigonometry 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Calculus 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Statistics (except for simple probability, arithmetic mean, and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 median) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following assumptions apply to all Q uantitative questions: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • All numbers used are real numbers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • All figures lie on a plane unless otherwise indicated. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • All lines shown as straight are straight. Lines that appear “ jagged” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can be assumed to be straight (lines can look somewhat jagged on 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the computer screen). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Additional assumptions about figures (diagrams and graphics) are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 different for Problem Solving questions than for Data Sufficiency 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 questions. (You’ll look at these assumptions when you examine each of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two formats just ahead.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving (22–23 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Problem Solving questions require you to work to a solution (a numerical 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value or other expression), and then find that solution among the five 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 Any of the Q uantitative areas listed on page 49 is fair game for a Problem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solving question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The directions on the following page are essentially what you’ll see during 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the pre-test tutorial and just prior to your first Problem Solving questions 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (you can access these directions at any time by clicking on the H ELP 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 button). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 51

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Directions: Solve this problem and indicate the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best of the answer choices given. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 N umbers: All numbers used are real numbers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Figures: A figure accompanying a Problem Solving 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 question is intended to provide information useful 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in solving the problem. Figures are drawn as accu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rately as possible EXCEPT when it is stated in a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 specific problem that its figure is not drawn to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scale. Straight lines may sometimes appear jagged. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 All figures lie on a plane unless otherwise indicated. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To review these directions for subsequent questions 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of this type, click on H ELP. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What Problem Solving Questions Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Let’s look at two Problem Solving questions that are similar to what you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might see on the GM AT. (Answer choices are lettered A–E here. Remember, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 though, that on the actual GM AT, you’ll select among choices by clicking 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on one of five blank ovals, not letters.) This first problem is easy to under- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 stand, and no formulas or tricky math is needed to solve it. Among GM AT 2 2 12345678901234567890123456789012123456789012345678901 test-takers, about 80% would answer this question correctly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Village A’s population, which is currently 6,800, is decreasing at a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rate of 120 each year. Village B’s population, which is currently 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4,200, is decreasing at a rate of 80 each year. At these rates, in how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 many years will the population of the two villages be equal? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 11 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 13 2 12345678901234567890123456789012123456789012345678901 D. 14 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 16 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. O ne way to solve this problem is to subtract 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 120 from A’s population while adding 80 to B’s population—again and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 again until the two are equal—keeping track of the number of times you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 perform these simultaneous operations. (You’ll find that number to be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13.) But there’s a faster way to solve the problem that also helps you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 avoid computation errors. The difference between the two populations is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 currently 2,600 (6,800 2 4,200). Each year that gap closes by 200 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (120 1 80). So you can simply divide 2,600 by 200 to determine the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number of years for the gap to close completely. That’s easy math: 2,600 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 200 5 13. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow here’s a more difficult Problem Solving question. To handle it, you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to understand rules involving exponents and their effect on the size 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and sign (positive or negative) of fractional numbers. Among GM AT 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 test-takers, only about 50% would respond correctly to this question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 k 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 If 227 5 , what is the value of k ? 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 29 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. 23 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. This question is asking you to determine the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 power that must be raised to in order to obtain 227. First, look at the 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 numbers in the question. N ote that 227 5 (23) . That’s a good clue that 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the answer to the question must involve the number 23. If the number we 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 were raising to the power of k were 23, then the value of k would be 3. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 But, the number we’re raising to the power is k is 2 , which is the 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reciprocal of 23. (By definition, the product of a number and its reciprocal 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 is 1.) So, you need to apply the rule that a negative exponent reciprocates 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 its base. In other words, raising a base number to a negative power is the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 same as raising the base number’s reciprocal to the power’s absolute value. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Therefore: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 23 2 12345678901234567890123456789012123456789012345678901 1 3 2 12345678901234567890123456789012123456789012345678901 5 (23) 2 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you can see, that value of k is 23. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the preceding questions, we’ve labeled the answer choices A through E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Remember that on the actual GM AT CAT screen, you’ll select your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice by clicking on one of five blank ovals (instead of choosing among 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 lettered answer choices). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 53

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Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Important features of the Problem Solving format to keep in mind (some of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these points are review). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • N umerical answer choices are listed in order—from smallest in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value to greatest in value. N otice in our first sample question that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the numerical values in the answer choices got larger as you read 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 down from A to E. That’s the way it is with every Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question whose answer choices are all numbers. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 There is one exception to this pattern. If a question asks you which 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 answer choice is greatest (or smallest) in value, the answer choices will not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily be listed in ascending order of value—for obvious reasons. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Some Problem Solving questions will include figures (geometry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 figures, graphs, and charts). M ost of the 528 geometry questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will be accompanied by some type of figure. Also, each Data 2 12345678901234567890123456789012123456789012345678901 Interpretation question will be accompanied by a chart or graph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Figures are drawn accurately unless the problem indicates other2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wise. Accompanying figures are intended to provide information 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 useful in solving the problems. They’re intended to help you, not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to mislead or trick you by their visual appearance. If a figure is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 not drawn to scale, you’ll see this warning near the figure: 2 12345678901234567890123456789012123456789012345678901 “ N ote: Figure not drawn to scale.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 It’s a whole different ball game when it comes to Data Sufficiency 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions, in which figures are not necessarily drawn to scale. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Data Sufficiency format is unique to the GM AT; you won’t find it on 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any other standardized test. Each Data Sufficiency consists of a question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 followed by two statements—labeled (1) and (2). Your task is to analyze 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each of the two statements to determine whether it provides sufficient data 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to answer the question and, if neither suffices alone, whether both 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 statements together suffice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency problems cover the same mix of arithmetic, algebra, and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 geometry as Problem Solving questions. (Any of the Q uantitative areas 2 2 12345678901234567890123456789012123456789012345678901 2 1 listed on page 49 is fair game for a Data Sufficiency question.) 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following directions are essentially what you’ll see during the pre-test 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tutorial and just prior to your first Data Sufficiency question. (You can 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 access these directions at any time by clicking on the H ELP button.) N otice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that some of the directions are new—in other words, they don’t apply to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving questions. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Directions: This Data Sufficiency problem consists of a question and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 two statements, labeled (1) and (2), in which certain data are given. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You have to decide whether the data given in the statements are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient for answering the question. Using the data given in the 2345678901234567890123456789012123456789012345678901 2 1 statements plus your knowledge of mathematics and everyday facts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (such as the number of days in July or the meaning of counterclock 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w ise), you must indicate whether: 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Statement 1 ALO N E is sufficient, but statement 2 alone is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient to answer the question asked; 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Statement 2 ALO N E is sufficient, but statement 1 alone is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient to answer the question asked; 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 BO TH statements (1) and (2) TO GETH ER are sufficient to answer 2 12345678901234567890123456789012123456789012345678901 the question asked; but N EITH ER statement ALO N E is sufficient; 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 EACH statement ALONE is sufficient to answer the question asked; 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Statements (1) and (2) TO GETH ER are N O T sufficient to answer 2 12345678901234567890123456789012123456789012345678901 the question asked, and additional data specific to the problem are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N umbers: All numbers used are real numbers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Figures: A figure accompanying a data sufficiency problem will 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conform to the information given in the question, but will not 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 necessarily conform to the additional information in statements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1 and 2). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lines shown as straight can be assumed to be straight and lines that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appear jagged can also be assumed to be straight. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You may assume that positions of points, angles, regions, etc., exist in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the order shown and that angle measures are greater than zero. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 All figures lie in a plane unless otherwise indicated. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ote: In Data Sufficiency problems that ask you for the value of a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 quantity the data given in the statements are sufficient only when it is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible to determine exactly one numerical value for the quantity. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To review these directions for subsequent questions of this type, click 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on H ELP. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 55

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What Data Sufficiency Questions Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As already noted, each Data Sufficiency consists of a question followed by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two statements labeled (1) and (2). Let’s look at two examples, similar to 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 what you’ll encounter on the GM AT. (Answer choices are lettered A–E 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here. Remember, though, that on the actual GM AT, you’ll select among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices by clicking on one of five blank ovals, not letters.) This first 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 question is a bit easier than average. O f all GM AT test-takers, about 85% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would respond correctly to it. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow many quarts of oil will a car burn during a 3,600 mile trip? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) The car burns half a quart of oil every 1,000 miles. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) At a price of $1.50 per quart, the car uses $2.70 worth of oil 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during the trip. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. Statement 1 ALO N E is sufficient, but statement 2 alone is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient to answer the question asked. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. Statement 2 ALO N E is sufficient, but statement 1 alone is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient to answer the question asked. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked; but N EITH ER statement ALO N E 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 is sufficient. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. EACH statement ALO N E is sufficient to answer the question 2 12345678901234567890123456789012123456789012345678901 asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem are needed. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. To answer the question, you need to know the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rate (the number of miles per quart) at which the car burns oil. Statement 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) provides the information you need. A half quart of oil is burned per 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1,000 miles; therefore, the car will burn 3.6 that amount over 3,600 miles. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although you don’t need to do the math, the answer to the question is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (3.6)(.5) 5 1.8. You’ve narrowed the answer choices to (A) and (D). But, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can you see that statement (2) alone also provides the information you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 need to determine the rate? The amount of oil used 5 $2.70 4 $1.50. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Again, although you don’t need to do the math, the quotient (and the 2 12345678901234567890123456789012123456789012345678901 2 answer to the question) is 1.8. Since either statement alone suffices to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question, the correct answer choice is (D). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This next Data Sufficiency question is a bit more difficult than average. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nly about 55% of all GM AT test-takers would respond correctly to it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What is the absolute value of the sum of two numbers? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) The product of the two numbers is 6. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) O ne number is 5 less than the other number. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Statement 1 ALO N E is sufficient, but statement 2 alone is not 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 sufficient to answer the question asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Statement 2 ALO N E is sufficient, but statement 1 alone is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sufficient to answer the question asked. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 2 12345678901234567890123456789012123456789012345678901 2 answer the question asked; but N EITH ER statement ALO N E 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is sufficient. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. EACH statement ALO N E is sufficient to answer the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 asked. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 problem are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. Calling one number x and the other number y, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 statement (1) alone tells us only that x y 5 6, but gives no information 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about their sum. This narrows the answer choice options to (B), (C), and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (E). Statement (2) alone tells us that the relationship between the two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbers can be written as y 5 x 25, but gives no information about their 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sum. The correct answer choice must be either (C) or (E). By considering 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 statements (1) and (2) together, you can substitute x 25 for y in the 2 12345678901234567890123456789012123456789012345678901 2 equation x y 5 6: 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x (x 2 5) 5 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 x 2 5x 5 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 2 5x 2 6 5 0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can factor the quadratic expression into two binomial factors, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find the roots of the equation—that is, the possible values of x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 2 6 5 0 or x 1 1 5 0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 5 6 or 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ence, either x 5 6 and y 5 1, with sum 7, or x 5 21 and y 5 26, with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sum 27. In either case, the absolute value of their sum is the same: 7. Since 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both statements together provide one and only one answer to the question, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the correct answer choice is (C). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can also analyze this problem less formally. Based on statement (1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 alone, try to think of some possibilities for the values of the two numbers 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that satisfy statement (1). Just using integers, the following four pairs 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 57

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 should occur to you: 1 and 6, 2 and 3, 21 and 26, or 22 and 23. Since 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 there’s more than one possibility, you can rule out answer choices (A) and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (D). Statement (2) alone presents an infinite number of possibilities, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 doesn’t it? So you can also rule out choice (B). Together, statements (1) and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) seem to rule out all integer pairs except (1, 6) and (21, 26). In either 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 case, the absolute value of their sum is 7. But what about non-integers? 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Answering this question is where a bit of intuition or trial-and-error is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 required. You may try a few non-integer number pairs, to satisfy you that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 none work. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Data Sufficiency 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Keep in mind the following important features of the Data Sufficiency 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 format (some of these points are review): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The answer choices are the same for all Data Sufficiency questions. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O ne feature that makes Data Sufficiency questions unique among 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 other types of GM AT questions is that the answer choices are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exactly the same for all Data Sufficiency questions. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Data Sufficiency questions can vary widely in difficulty level. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Assuming you’re familiar with their unique format, these questions 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 are neither inherently easier nor more difficult than Problem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solving questions. The level of difficulty and complexity can vary 2 12345678901234567890123456789012123456789012345678901 widely (depending on the correctness of your responses to earlier 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A Data Sufficiency question that asks for a specific numerical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value is answerable only if one and only one value results. Some, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 but not all, Data Sufficiency questions will ask for a particular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 num erical value. For example: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What is the area of the circle? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What is the value of x ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • What is the area of triangle A BC? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • H ow much did Sam pay for his book? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You must keep in mind that in any Data Sufficiency question, if the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choices consist of numerical values only (no variables), then the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question is answerable only if one and only one value results—not a range 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of numbers, not a positive or negative number, not an expression that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 includes a variable. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The two statements (1 and 2) will not conflict with each other. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Perhaps you’re wondering which response you should choose—(D) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or (E)—if you can answer the question with either statement alone, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 but get two conflicting answers. Don’t worry; this won’t happen. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you can answer the question using either statement alone, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answ er w ill be the sam e in both cases. In other words, statements 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1 and 2 will never conflict with one another. Why? The test2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 makers design Data Sufficiency questions to avoid the “ D vs. E” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 conundrum. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Figures are not necessarily drawn to scale, unless noted otherwise. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Any figure accompanying a Data Sufficiency question will conform 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the information in the question itself, but will not necessarily 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conform to either statement 1 or 2. So although the figures are not 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 designed to mislead you, they are not necessarily drawn to scale. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Data Sufficiency questions, just like in Problem Solving questions, rely 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the information in the question and statements, not on a figure’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 appearance. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Calculating is not what Data Sufficiency is primarily about. Expect 2 12345678901234567890123456789012123456789012345678901 2 to do far less number crunching and equation solving for Data 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sufficiency questions than for Problem Solving questions. What’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 being tested here is your ability to recognize and understand 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 principles, not to work step-by-step toward a solution. (That’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what Problem Solving is about.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Verbal Ability Section 2 12345678901234567890123456789012123456789012345678901 2 1 (41 Questions, 75 Minutes) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Verbal Ability section contains questions in three distinct formats: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Critical Reasoning (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Sentence Correction (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Reading Comprehension (12–13 questions) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Regardless of the format, each and every question in the Verbal Ability 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 section is five-choice multiple-choice. O therwise, each of the three formats 2 2 12345678901234567890123456789012123456789012345678901 is quite distinct. In the pages ahead, you examine each one up close. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 59

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning questions are designed to measure your ability to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 understand, criticize, and draw reasonable conclusions from arguments. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s Covered 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 GM AT Critical Reasoning questions cover various aspects of reasoning 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and evaluating arguments. H ere are the three basic aspects on which m ost 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the exam’s 14–15 Critical Reasoning questions are based: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Identifying assumptions underlying an argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Understanding the effect of additional evidence on an argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Drawing strong inferences from stated premises 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Some GM AT Critical Reasoning questions will involve specific forms of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning or argument evaluation. Look for any of the following forms on 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 your exam: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognizing a hypothesis that provides a good explanation for a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set of observations 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognizing an effective strategy, based on a set of premises and a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stated objective 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • M aking valid deductions from stated premises, or recognizing an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional premise needed to validate a stated conclusion 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognizing similarities in reasoning between different arguments 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 There are no special instructions for GM AT Critical Reasoning. The 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 following simple directions are essentially what you’ll see during the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pre-test tutorial and just prior to your first Critical Reasoning question 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (you can access these directions at any time by clicking on the H ELP 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 button): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Directions: For this question, select the best of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices given. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What Critical Reasoning Questions Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each Critical Reasoning question consists of a paragraph-length passage, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 followed by a question about the passage and five answer choices. Let’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 look at two Critical Reasoning questions that are similar to what you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might see on the GM AT. (Answer choices are lettered A–E here. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Remember, though, that on the actual GM AT you’ll select among choices 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by clicking on one of five blank ovals, not letters.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This first question is a bit easier than average; among GM AT test-takers, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about 80% would answer it correctly. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ten years ago, Brand 1 was the most popular beer among consumers. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Today, however, consumers spend twice the amount on Brand 2, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another brand of beer, than on Brand 1, even though Brand 2 is nearly 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 twice as expensive as Brand 1. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following, if true, would best explain the apparent 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 discrepancy described above? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Consumers of beer as a group consider a beer’s taste more 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 important than its price. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Brand 2 beer has decreased in price over the last ten years. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. O ver the last ten years, wine has become a more popular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 beverage among consumers than beer. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. Brand 2 beer is more readily available to consumers today than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Brand 1 beer. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The minimum age at which a person can legally drink beer is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 lower today than ten years ago. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The best answer choice must explain why 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Brand 2 beer is more popular than Brand 1 beer despite its higher price. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 O nly choice (D) provides an adequate explanation. If Brand 1 beer is not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 available, while Brand 2 is, then obviously a consumer will purchase Brand 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 and not Brand 1. Choice (A) might explain the discrepancy if consumers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 prefer the taste of Brand 2 beer over that of Brand 1 beer; however, we 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t know whether this is the case. Choice (B) might explain an increase 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in sales of Brand 2 beer; however, it fails to explain why Brand 2 is more 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 popular today than Brand 1. Choice (C) might explain declining beer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 consumption generally; however, the popularity of wine is irrelevant to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 popularity of one brand of beer compared to another brand of beer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Choice (E) might explain an increase in beer sales generally, but it does not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explain why consumers buy more Brand 2 beer than Brand 1 beer. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This next Critical Reasoning question is a bit more difficult than average. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nly about 50% of all GM AT test-takers would respond correctly to it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Com pany Spok esperson: Charges that our corporation has discrimi- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 nated against women in its hiring and promotion practices are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 demonstrably untrue. In fact, statistics show that greater than sixty 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 percent of our corporation’s employees are women. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 61

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The answer to which of the following questions would be most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relevant in evaluating the argument above? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. What is the average tenure, or length of employment, among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the company’s women employees? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. What percentage of the company’s employees in higher-level 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 management positions are women? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. What percentage of employees in competing companies are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 women? 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. H ow has the percentage of women employees at the company 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 changed over time? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 E. Is the chief executive officer of the company a man or a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 woman? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. What makes this question difficult is that some 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 of the incorrect answer choices are somewhat relevant to the argument; 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but their relevance is neither as clear nor as direct as choice (B). Let’s start 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with the correct answer. Although a large percentage of the company’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 employees are women, it is entirely possible that these women generally 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occupy low-level positions while male employees generally hold higher- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 level jobs. O ne possible explanation for such a discrepancy would be that, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 when deciding whom to promote, the company discriminates against 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 women. H ence, the answer to the question in choice (B) is highly relevant 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to evaluating the spokesperson’s denial that the company engages in this 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 type of discrimination. The issue raised in choice (A) would be relevant to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whether the company’s employee-termination practices are discrimina12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tory, especially if the average tenure for women turned out to be 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 significantly briefer than for men. H owever, the issue of tenure is not 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 directly relevant to the company’s hiring or promotion practices. N or is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the issue raised in choice (C) directly relevant to the argument. For 2 2 12345678901234567890123456789012123456789012345678901 example, assume that the percentage of the company’s employees that are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 women is typical among firms in its industry. So what? Perhaps all of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 firms discriminate against women, or perhaps none do. As for choice (D), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the company’s practices in the past are not directly relevant to its current 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 practices. Choice (E) focuses on only one high-level employee, hardly a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sufficient statistical sampling to prove a pattern of discrimination. Also, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 even with a female CEO , a company could very well engage in hiring and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 promotion practices that are unfair to women. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind the following important features of Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Your knowledge of the topic at hand is not important in answering 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning questions. The test-makers design Critical 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Reasoning questions so that you can analyze and answer them 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without regard to what is factual (or not) in the real world. Also, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whatever your personal opinions or viewpoints about the issue 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 that an argument raises, they are irrelevant to analyzing the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument and answering the question. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Distinctions in quality between answer choices can be subtle. 2 12345678901234567890123456789012123456789012345678901 GM AT Critical Reasoning is not a “ black-and-white” affair in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which one answer is perfect while each of the others is completely 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 wrong. A typical Critical Reasoning question stem contains a word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 such as “ best” or “ most.” That’s because more than one answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice usually has merit—it’s just that the correct answer choice is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the strongest among the bunch. (To master GM AT Critical 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Reasoning, you’ll need to become comfortable with these shades 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of gray.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Each piece of information in the paragraph is usually important in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answering the question. O ccasionally, a Critical Reasoning 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 paragraph will include superfluous information, which does not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 come into play at all in analyzing the argument and answering the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. But this is the exceptional case. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence Correction (14–15 questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence Correction questions are designed to measure your command of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the English language and of the conventions of Standard Written English. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 GM AT Sentence Correction covers two areas of English language 2 2 12345678901234567890123456789012123456789012345678901 proficiency: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Correct ex pression, measured by your ability to recognize errors 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in grammar, diction, and word usage 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Effective ex pression, measured by your ability to improve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentences that are poorly worded or structured 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 63

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GM AT Sentence Correction does N O T cover these other areas of English 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 language proficiency: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Punctuation (except that comma placement can come into play if 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it affects the meaning of a sentence) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2. Vocabulary (you won’t have to memorize long lists of obscure 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 words just for GM AT Sentence Correction) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Slang and colloquialism s (informal expressions don’t appear at 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 all in Sentence Correction questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test Directions 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 The following set of directions are essentially what you’ll see during the 2 2 12345678901234567890123456789012123456789012345678901 pre-test tutorial and just prior to your first Sentence Correction question (you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can access these directions at any time by clicking on the H ELP button): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Directions: This question presents a sentence, all 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or part of which is underlined. Beneath the sen2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tence you will find five ways of phrasing the under2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lined part. The first of these repeats the original; the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 other four are different. If you think the original is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best, choose the first answer; otherwise, choose one 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 of the other answers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This question tests correctness and effectiveness of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expression. In choosing your answer, follow the re12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 quirements of Standard Written English; that is, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pay attention to grammar, choice of words, and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sentence construction. Choose the answer that pro2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 duces the most effective sentence; this answer 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 should be clear and exact, without awkwardness, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ambiguity, redundancy, or grammatical error. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What Sentence Correction Questions Look Like 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In each Sentence Correction question, part of a sentence (or the whole 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence) will be underlined. The first answer choice will simply restate the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 underlined part “ as is.” The other four choices present alternatives to the 2 12345678901234567890123456789012123456789012345678901 2 2 original underlined phrase. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Let’s look at two questions that are similar to what you might see on the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 GM AT. (Answer choices are lettered A–E here. Remember, though, that on 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the actual GM AT you’ll select among choices by clicking on one of five 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 blank ovals, not letters.) This first question is a bit easier than average; 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among GM AT test-takers, about 80% would answer this question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correctly. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A thesaurus can be a useful tool for writers, providing he knows 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 how to use it correctly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. writers, providing he knows how to use it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. writers, providing he knows how to use such a book 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. a writer, providing he knows how to use them 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 D. writers, providing she knows how to use it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. writers, providing they know how to use it 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The correct answer is E. A pronoun and the noun to which it refers 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (called the antecedent) should be consistent; both should be either singular 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 or plural. In the original sentence, however, the singular pronoun he is 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 inconsistent with its plural antecedent w riters. Among the four alterna- 2 2 12345678901234567890123456789012123456789012345678901 tives, only choices (C) and (E) fix this problem. In choice (C), both are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 singular, while in choice (E) both are plural; either is acceptable. Choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (C), however, creates another pronoun-antecedent error. N otice that it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 replaces the singular pronoun it with the plural them . Since the intended 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 antecedent is thesaurus, which is singular, the plural pronoun them is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect, and you can eliminate choice (C). Choice (E) is the best version 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of the underlined part; it fixes the problem with the original version 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without creating any new errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s a Sentence Correction question that’s a bit more difficult than 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 average. O f all GM AT test-takers, only about 55% would respond 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correctly to it. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Frank Lloyd Wright was a preeminent architect of the twentieth 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 century, and there have been many less talented people who, both in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the past and today, have imitated his style. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. there have been many less talented people who, both in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 past and today, have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. a great number of less talented people of today, as well as in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the past, have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. many less talented people, both in the past and today, have 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. there are many less talented people, today as well as in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 past, who 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 E. many people less talented than Wright who, today as well as in 2 12345678901234567890123456789012123456789012345678901 22 the past, have 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. The original version contains no grammatical 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 errors. H owever, the phrase there have been m any less talented people w ho 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is wordy. Choice (C) provides a more concise and graceful version, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without introducing any new errors. In choice (B), a great num ber of is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 wordy; also, the two phrases of today and in the past lack grammatical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 parallelism. Choice (D) provides a less wordy version than the original, but 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 65

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 is still not as effective as choice (C). As for choice (E), it too is unnecessarily 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wordy; what’s more, within the construction of choice (E), the word w ho 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 creates an incomplete sentence and should be omitted. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Sentence Correction 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Keep in mind the following important features of Sentence Correction 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions (some of these points are review): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Any part of the sentence might be underlined. The underlined part 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 may appear at the beginning, middle, or end of the sentence. Also, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in some cases, the entire sentence will be underlined. Expect all of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 these variations on your exam. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The first answer choice simply restates the underlined part “as is.” 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The other four choices present alternatives to the original under2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lined phrase. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The best answer choice isn’t always perfect. The best choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among the five will not contain any grammatical errors. H owever, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it may make for a less-than-ideal sentence, at least in your opinion. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But remember: You’re looking for the best version of the five, not 2 12345678901234567890123456789012123456789012345678901 the perfect version. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • More than one answer choice may be grammatically correct. These 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions cover not just grammar, but also effective expression. So 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 don’t select an answer choice just because it results in a grammati2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cally correct sentence. Another answer choice may be clearer, more 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise, or less awkward—and therefore better. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A single Sentence Correction item can cover a lot of ground. Don’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expect each Sentence Correction item to isolate and test you on 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 one, and only one, rule of grammar or aspect of written expres2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sion. Typically, by the time you’ve read all five choices, you’ve seen 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a variety of grammatical errors and other problems—at least 2 12345678901234567890123456789012123456789012345678901 among the four incorrect choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Punctuation doesn’t matter. You won’t find errors in punctuation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in these sentences (except as part of larger errors involving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence structure). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • You won’t need any knowledge of the topic at hand in order to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 handle a question. You’re at no disadvantage if you know little or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 nothing about the topic of any particular sentence. For instance, in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 handling the second question above, experts on Frank Lloyd 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Wright would not have any advantage over other test-takers, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would they? 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Reading Comprehension (12–13 questions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Reading Comprehension questions are designed to measure your 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ability to read carefully and accurately, to determine the relationships 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 among the various parts of the passage, and to draw reasonable inferences 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from the material in the passage. O n the GM AT, you’ll encounter four sets 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of Reading Comprehension questions; all questions in a set pertain to the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same passage and are presented in sequence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 What’s Covered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Reading Comprehension tests on the following reading skills (you 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 can think of these skills as question types): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Recognizing the main point or primary purpose of the passage 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Recalling information explicitly stated in the passage 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M aking inferences from specific information stated in the passage 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Recognizing the purpose of specific passage information 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Applying and extrapolating from the ideas presented in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Test Directions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following set of directions are essentially what you’ll see during the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 pre-test tutorial and just prior to your first group of Reading Comprehen- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sion questions (you can access these directions at any time by clicking on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the H ELP button): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Directions: The questions in this group are based 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the content of a passage. After reading the pas12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sage, choose the best answer to each question. An2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 swer all questions on the basis of what is stated or 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 im plied in the passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What Reading Comprehension Sets Look Like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each Reading Comprehension set consists of a reading passage along with 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a series of 3–4 questions about the passage. H ere’s a typical passage. Go 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ahead and read it now. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Line Urodeles, a class of vertebrates that includes small, lizard-like 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 creatures such as newts and salamanders, have an enviable 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ability to regenerate arms, legs, tails, heart muscle, jaws, spinal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cords, and other organs that are injured or destroyed by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accidents or those who prey on them. Planaria, which are a (5) 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 67

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 type of simple worm, have their own form of regenerative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 power. A single worm can be sliced and diced into hundreds of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pieces, each piece giving rise to a completely new animal. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 H owever, while both urodeles and planaria have the capacity 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to regenerate, they use different means to accomplish this feat. (10) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In effect, urodeles turn back the biological clock. First, the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 animal heals the wound at the site of the missing limb. Then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 various specialized cells at the site, such as bone, skin, and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 blood cells, lose their identity and revert to cells as unspecial2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ized as those in the embryonic limb bud. This process is called (15) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dedifferentiation, and the resulting blastema, a mass of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 unspecialized cells, proliferates rapidly to form a limb bud. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ultimately, when the new limb takes shape, the cells take on 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the specialized roles they had previously cast off. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In contrast, planaria regenerate using cells called neoblasts. 2 (20) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Scattered within the planarian body, these neoblasts remain in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an unspecialized, stem-cell state, which enables them at need to 2 2 12345678901234567890123456789012123456789012345678901 differentiate into any cell type. Whenever planaria are cut, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 neoblasts migrate to the site and form a blastema by them12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (25) selves. It is interesting to note that this mechanism is similar to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that following reproductive fission in these animals, and that 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 species incapable of this form of asexual reproduction have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 poorly developed regenerative capacities. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, look at two questions based on the preceding passage. (Answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices are lettered A–E here. Remember, though, that on the actual 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT you’ll select among choices by clicking on one of five blank ovals, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not letters.) This first question is a bit easier than average; among GM AT 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 test-takers, about 80% would answer this question correctly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The author’s primary purpose in the passage is to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. describe the roles of blastema in regenerating urodeles and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 planaria. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. describe how urodeles use the process of dedifferentiation to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regenerate. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. contrast the mechanisms by which urodeles and planaria 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 accomplish regeneration. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. show how methods of cellular regeneration have evolved in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 different animal species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. explain the link between reproductive fission and regeneration 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in simple worms. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 2: The GM AT—Up Close

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The last sentence of the first paragraph sets 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forth this central theme: that urodeles and planaria differ in the means they 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use to regenerate. The paragraphs that follow provide the details that 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 reveal those differences. The second paragraph discusses how urodeles 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regenerate, while the third paragraph discusses how planaria regenerate. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (N otice the phase “ In contrast,” which begins the third paragraph.) Each 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 of the incorrect choices distorts the author’s central focus in the passage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a question that’s a bit more difficult than average. O f all GM AT 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 test-takers, only about 50% would respond correctly to it. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the final sentence of the passage (lines 25–28), the author implies that 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. reproductive fission and regeneration in certain planaria differ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solely in the quantity of new planaria produced. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. planaria that reproduce sexually use the process of dedifferen2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tiation to regenerate entirely new animals. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. asexual reproduction is related to regeneration in planaria but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not in urodeles. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. the genetic makeup of planaria created through regeneration 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would be the same as in those created through reproductive 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 fission. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. those planaria that reproduce by splitting themselves in two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are more likely to regenerate using the same mechanism. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is E. The idea in the final sentence of this passage is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficult to grasp, making this question difficult to answer. The sentence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 says essentially that those species of planaria that do not engage in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reproductive fission (i.e., splitting) are more likely to regenerate them- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 selves in this way than those species of planaria that do. Choice (E) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 expresses the same essential idea conversely: species of planaria that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reproduce asexually (by fission, or splitting) are the ones that are more 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 likely to be able to regenerate in the same way. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Key Facts about GMAT Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind the following important features of GM AT Reading 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Comprehension (some of these points are review): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Passages appear on the left side of the computer screen, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions appear (one at a time) on the right side. You’ll have to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 scroll vertically to read each entire passage, even the short ones (as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the simulated screen shot on page 21). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Reading Comprehension questions are designed to test a lot more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than just your short-term memory and your knack for finding in2 12345678901234567890123456789012123456789012345678901 2 1 formation quickly. Although your ability to recall what you’ve 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 69

Part I: Everything You Ever W anted to Know about the G M AT

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 read is part of what’s being tested, all but the easiest questions also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 gauge your ability to assimilate, interpret, and apply the ideas 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 presented. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Some questions require that you focus on an isolated sentence or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two; others require that you assimilate information from various 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 parts of the passage. Understandably, questions that cover dispar2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ate parts of a passage tend to be tougher than ones that you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer just by reading a particular sentence or two. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Questions about information appearing early in the passage tend 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to come before other questions. H owever, this isn’t a hard-and-fast 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 rule; don’t assume you can simply scroll down the passage to 2 12345678901234567890123456789012123456789012345678901 answer each question in turn. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Tougher questions include not only a “best” response but also a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tempting second-best response. Recognizing the difference in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 quality between the two most viable responses is the key to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answering the questions correctly. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Reading Comprehension questions are not designed to test your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 vocabulary. Sure, you’ll find the occasional advanced, technical, or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 obscure word. But the test-makers don’t intentionally load the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passages with tough vocabulary. Also, if a reading passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 introduces a technical term, don’t worry—the passage will supply 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 all you need to know about the term to respond to the questions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Reading Comprehension passages are condensed from larger 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 works in the humanities, social sciences, and physical sciences. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Specific sources include professional journals, dissertations, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 periodicals of intellectual interest. The test-makers edit the source 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 material in order to pack it with test-worthy material. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • All reading passages are not created equal—that is, equally 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficult. Comparatively tough passages are typically written in a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 dryer, more “ academic” style than easier ones. Syntax is more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 complex, and vocabulary more advanced. The passage’s topic 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might deal with ideas and concepts that are more difficult to grasp, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or it might be written, organized, or edited in a way that makes it 12345678901234567890123456789012123456789012345678901 2 2 more difficult to assimilate. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Prior knowledge of a passage’s subject matter is not important. All 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions are answerable based solely on information in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage. The exam includes passages from a variety of disciplines, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 so it is unlikely that any particular test-taker knows enough about 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 two or more of the areas included on the test to hold a significant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 advantage over other test-takers. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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PART

II Analytical Writing Assessment Analytical Writing Assessment

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PART II

Chapter

3 Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to Analytical Writing Assessment. At this point, you’ll learn the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basics about writing effective GM AT Issue-Analysis and Argument- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Analysis essays—ones that will earn you a better-than-average Analytical 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Writing Assessment score of at least 4 on the 0–6 scale. Specifically, you 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 will learn the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A step-by-step approach to brainstorming, organizing, composing, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and proofreading your essays, all comfortably within the 3012345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 minute time limit for each writing task 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Success keys to scoring higher with your essays than most GM AT 2 12345678901234567890123456789012123456789012345678901 test-takers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Useful tips for writing mechanics and for developing a writing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 style that’s appropriate for the GM AT 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—Your 7-Step Game Plan 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 For a high-scoring Issue essay, you need to accomplish these four basic 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tasks: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Recognize and deal with the complexities and implications of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. O rganize, develop, and express your ideas in a coherent and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 persuasive manner. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Support your ideas with sound reasons and relevant examples. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Demonstrate adequate control of the elements of Standard 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Written English (grammar, syntax, and usage). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The 30 minutes you’re allowed to write your Issue essay isn’t much time, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 so you will need to use the time wisely. This does not mean using every one 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 of your 30 minutes to peck away at the keyboard like mad. You should 2 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 72

N ote

Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 spend some time up front thinking about what you should write and how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you should organize your ideas. And you should save some time at the end 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to proofread and fine-tune your essay. H ere’s a 7-step game plan to help 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 you budget your time so you can accomplish all four tasks listed above 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 within your 30-minute time limit (suggested times are parenthesized): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 1. Brainstorm and make notes (3 min.). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Review your notes, and decide on a viewpoint (1 min.). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3. O rganize your ideas into a logical sequence (1 min.). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Compose a brief introductory paragraph (2 min.). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 5. Compose the body of your response (16 min.). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. Compose a brief concluding or summary paragraph (2 min.). 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7. Proofread for significant mechanical problems (5 min.). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that, by following the suggested times for each step, you’ll spend 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 about 5 minutes planning your essay, 20 minutes writing it, and 5 minutes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 proofreading it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These suggested time limits for each step are merely guidelines, not 2 12345678901234567890123456789012123456789012345678901 hard-and-fast rules. As you practice composing your own Issue essays 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 under timed conditions, start with these guidelines; then, adjust to a pace 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that works best for you. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the following pages, you’ll walk through each step in turn, applying the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following Issue statement, which is similar to some of the statements in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 official pool 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Issue Statement 1 (and directive) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Schools should be responsible not only for teaching academic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 skills but also for teaching ethical and social values.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Discuss the extent to which you agree or disagree with the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 foregoing statement. Support your perspective using reasons 2 2 12345678901234567890123456789012123456789012345678901 and/or examples from your experience, observation, reading, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 academic studies. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Brainstorm and Make Notes (3 min.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Your first step in developing your Issue essay is to brainstorm for ideas that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are relevant to the topic. Try to think of some reasons and examples 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 supporting not just one side, but both sides, of the issue. As you conjure up 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 ideas, don’t commit to a position on the issue, and don’t try to filter out 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 73

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 what you think might be unconvincing reasons or weak examples. Just let 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 all your ideas flow onto your scratch paper, in no particular order. (You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can sort through them during steps 2 and 3.) H ere’s what a test-taker’s 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 notes for Issue statement 1 on page 73 might look like after a few minutes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of brainstorming: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Whose values? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Amish 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suburbanites 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yuppies 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Southern Baptists 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pluralism 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 schools need focus 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sex education 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 classroom cooperation vs. competition 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 teachers set examples—indirectly 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 drugs & violence 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that the first several lines reflect one train of thought (If schools 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 were to teach ethical values, whose values would they teach?) while the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other notes reflect other random ideas. The notes are somewhat of a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hodgepodge, but that’s okay. The point of brainstorming is just to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 generates a bunch of ideas—the raw material for your Issue essay. Let your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ideas flow freely, and you’ll have plenty of fodder for that essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Review Your Notes, and Decide on a Viewpoint 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1 min.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Decide on the basic point of view (either “ pro” or “ con” ) you want to 2 2 12345678901234567890123456789012123456789012345678901 defend in your essay. In other words, decide whether you are going to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basically agree or disagree with the statement. Your notes from step 1 should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 help you decide. Review the ideas you jotted down, and then ask yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whether you can make a stronger case for or against the statement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind: There is no “ correct” viewpoint or position on any GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 issue. So don’t waste time debating over what viewpoint you should 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 defend. Just go with the flow—choose whatever viewpoint seems easiest 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or most “ natural” for you to defend. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ext, pick the three or four ideas from your notes that best support your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 viewpoint. These should be ideas that you think make sense, that support 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your viewpoint reasonably well, and that you know enough about to write 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 at least a few sentences on. Put a checkmark next to these ideas, to signify 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that they are the ones you’re certain you want to use in your essay. If there 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 aren’t enough ideas, take one or two of the ideas you like and elaborate on 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 them. Think of related ideas, add details or examples, and use these to fill 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 out your list. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 It’s perfectly acceptable to strongly agree or disagree with the Issue 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement. But it’s also okay to qualify the statement, which means that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 your agreement (or disagreement) with it is less than complete. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Organize Your Ideas into A Logical Sequence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1 min.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, decide on a sequence for the ideas. The best sequence might be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 obvious. O ne idea may lead logically to another. Your ideas might involve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 historical examples, which lead chronologically from one to another. O r, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your ideas might range from the personal level to the family or community 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 level, then to the societal or global level. Any of these schemes suggests a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 certain natural sequence for your Issue essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If there’s no obvious sequence, one effective approach is to decide which 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two ideas you like best—the two you consider most convincing or that you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 happen to know the most about and can develop most fully—and earmark 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 these ideas to discuss first and last (in either order) in the body of your 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 essay. Then sequence the remaining ideas in any order, but betw een your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two best ideas. Why sequence your ideas this way? The most emphatic and 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 memorable parts of any essay are its beginning and end. It makes sense 2 12345678901234567890123456789012123456789012345678901 that your best material should go there, where it will have the greatest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible impact on the reader. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The suggested sequence on page 76 is a basic one that works well in many 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cases. But there are a myriad of other effective ways to organize ideas for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 your Issue essay. At the N ext Level, you’ll explore some of these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternatives. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 75

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O nce you’ve decided on a sequence for your ideas, number them 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accordingly in your notes. H ere’s an example of how a test-taker might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 turn the notes on statement 1 into a simple outline: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. U Whose values? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Amish 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suburbanites 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 yuppies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Southern Baptists 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1. U pluralism 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. U schools need focus 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sex education 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 classroom cooperation vs. competition 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 teachers set examples-indirectly 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 drugs & violence 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. U U.S. Schools lag 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that this test-taker has decided to essentially disagree with the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement—that is, to take the position that schools should teach 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 academics only and not ethical values. The first three points in his notes all 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fit nicely into an argument for this viewpoint. H e also thought of a fourth 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 idea that he thought might make a good ending—that U.S. schools lag 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 behind most other countries in academic standards, and so time must not 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be taken away from teaching academic subjects to teach ethics. So he made 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a note of that idea, and checked it off as well. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H e decided to start with the idea that America is pluralistic. From this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 idea, it makes sense to ask, “ Whose values would be taught in schools?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and use the examples listed. This leads nicely into the point about focusing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on academics and, finally, the argument about how U.S. students lag 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 behind others. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Compose a Brief Introductory Paragraph (2 min.) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you’ve spent about five minutes planning your essay, its time to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compose it. You’ll begin with a brief introductory paragraph, in which you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 should accomplish the following: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Demonstrate that you understand the issue that the statement 2 2 12345678901234567890123456789012123456789012345678901 raises. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Let the reader know that you have a clear viewpoint on the issue. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Anticipate the ideas you intend to present in your essay’s body 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 paragraphs. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can probably accomplish all three tasks in 2–3 sentences. In your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 introductory paragraph, don’t go into detail about your reasoning, and 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 don’t provide specific examples. This is what the body paragraphs of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay are for. Also, don’t begin your introductory paragraph by repeating 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 the statement verbatim. This amounts to wasted time, since the reader is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 already familiar with the topic. Instead, show the reader from the very first 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence that you’re thinking for yourself. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 H ere’s an introductory paragraph for statement 1—based on the test- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 taker’s outline on page 76: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Introductory paragraph (Issue Statement 1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Schools, especially in a pluralistic nation such as the United States, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 should limit what they teach to academic subjects—leaving it to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parents and clergy to teach ethics. To do otherwise, as the statement 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 suggests, is to invite trouble, as this essay will show. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. Compose the Body of Your Essay (16 min.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During step 4, your chief ambition is to get your main points—and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 supporting reasons and examples—from your brain and your scratch 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 paper onto the computer screen! H ere’s what you need to keep in mind as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you compose your body paragraphs: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Be sure the first sentence of each paragraph begins a distinct train 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of thought and clearly conveys to the reader the essence of the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Arrange your paragraphs so that your essay flows logically and 2 12345678901234567890123456789012123456789012345678901 persuasively from one point to the next. Stick to your outline, but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be flexible. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Try to devote at least two, but no more than three or four, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentences to each main point in your outline. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Don’t worry if you don’t have time to include every single point 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from your outline. The readers understand that time constraints 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 prevent most test-takers from covering every point they want 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to make. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Don’t stray from the issue at hand, or from the points you seek to 2 12345678901234567890123456789012123456789012345678901 make. Be sure to stay well focused on both. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 77

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, here are the body paragraphs of a response to statement 1—based on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the outline on page 76: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Four-paragraph body (Issue Statement 1) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If our schools are to teach values, the most important question to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer is: Whose values would they teach? After all, not all ethical 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 values are the same. The Amish have a way of life that stresses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simplicity and austerity; they shun modern conveniences and even 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 such activities as dancing. By contrast, the typical young urban 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 family—“ yuppies,” as they’re often called—enjoys buying the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 latest electronic gadgets and going on expensive vacations. Either 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 group might be offended by the values of the other. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 True, Amish and yuppie children aren’t likely to attend the same 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 schools; but what about children from Jewish and fundamentalist 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Christian households? These two religious groups may live in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same town or neighborhood, and either one might very well be 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incensed if the other group’s moral teachings were imposed on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The only way to avoid the inevitable conflicts that teaching ethics 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 would bring to our schools is by allowing teachers to focus on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what they’re paid to do: teach academics. We send children to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 school to learn math, English, history, and science. H ow would we 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 feel if our kids came home ignorant about geometry but 2 2 12345678901234567890123456789012123456789012345678901 indoctrinated with someone else’s religious or ethical ideas? Justly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 annoyed, I think. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M oreover, consider that schoolchildren in the U.S. lag behind 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 those in most other nations in academic achievement. In light of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this fact, it would seem foolish for us to divert classroom time from 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 teaching academics to teaching “ morality.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice the following features of these body paragraphs, which show that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the test-taker tried to stick to his outline, while at the same time remaining 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 flexible as new ideas for content or organization occurred to him: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Point 2 in the outline (“ Whose values?” ) became the basis for tw o 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraphs (the second and third ones), not just one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • After writing about the Amish and yuppies, the test-taker seemed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to realize that the contrast between them, while illustrating the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 point, was a bit exaggerated. Rather than replacing the entire 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph with a more realistic pairing, which would have meant 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 substantial time wasted, the test-taker added the third paragraph 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to provide a more down-to-earth pairing. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The suburbanites got left out of the essay altogether, possibly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because they seemed unnecessary. (O r, perhaps the test-taker 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 realized that he was running short on time.) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. Compose a Brief Concluding or Summary 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Paragraph (2 min.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Unless your essay has a clear ending, the reader might think you didn’t 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 finish in time. That’s not the impression you want to make; so be sure to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 make time to wrap up your discussion. Convey the main thrust of your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay in a clear, concise, and assertive way. Two or three sentences should 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 suffice. If an especially insightful concluding point occurs to you, the final 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence of your essay is a good place for it. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s a brief but effective concluding paragraph for the essay on Issue 2 12345678901234567890123456789012123456789012345678901 statement 1. N otice that it assures the reader that the test-taker has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 organized his time well and finished the writing task. Also, notice that this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 brief summary does not introduce any new reasons or examples; it’s just a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quick recapitulation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Final paragraph (Issue Statement 1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Ironically, what is most ethical for our schools to do in the interest 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of educating our children is to avoid becoming entangled in ethical 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 issues. Stick to academics, and let families and clergy teach 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 morality in their own way and on their own time. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7. Proofread for Glaring Mechanical Problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (5 min.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To score high on your Issue essay, you don’t need to compose a flawless 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 work of art. The readers won’t reduce your score for the occasional 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 awkward sentence and minor error in punctuation, spelling, grammar, or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 diction (word choice and usage). Don’t get hung up on whether each 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence is something your English composition professor would be proud 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of. Instead, use whatever time remains to read your essay from start to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 finish and fix the most glaring mechanical problems. H ere are some 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggestions for what you should and, just as importantly, what you should 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 not, try to accomplish during this final step: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Find and rework awkward sentences, especially ones where the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point you’re trying to make is not clear. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Find and correct accidentally omissions of words, garbled phrases, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 grammatical errors, and typographical errors. It doesn’t take much 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 79

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 time to fix these kinds of errors, and the time spent will go a long 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way toward making a positive impression on the reader. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Correct spelling errors only when they might prevent the reader 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from understanding the point at hand. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Don’t spend any of your valuable time correcting punctuation or 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 removing extra character spaces between words. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Don’t get drawn into drastic rewriting. Accept that your essay is 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 what it is and that you don’t have time to reshape it substantially. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 From beginning to end (including the introductory, body, and concluding 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 paragraphs), the preceding sample essay runs just over 300 words in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 length. It is neither lengthy nor a literary masterpiece. N evertheless, it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expresses a clear viewpoint, it’s smartly organized, it employs relevant 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasons and examples, and it’s crisp and effective in style. In short, it 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contains all the elements of a high-scoring GM AT Issue essay. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for Writing a GMAT Issue2 12345678901234567890123456789012123456789012345678901 2 1 Analysis Essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s our very best advice for GM AT Issue Analysis, parsed out into 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 bite-size pieces. Some of these tips reiterate suggestions made earlier in this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lesson—suggestions that are well worth underscoring. O thers are new 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here. Apply these points of advice to Part V’s practice tests, and then 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 review them again, just before exam day. You’ll be glad you did! 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Adopt a Viewpoint . . . Any Viewpoint 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 It’s perfectly acceptable to strongly agree or disagree with an Issue 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement. Don’t worry that your position may appear somewhat 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ right-wing” or “ left-wing,” or even outside the mainstream altogether. 2 2 12345678901234567890123456789012123456789012345678901 Just be sure to provide sound reasons and relevant examples to justify your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strong viewpoint. It’s also perfectly okay to qualify the statement—in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other words, to accept (or reject) it only in part or to a limited extent. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Again, just be sure to justify your “ middle-ground” position with sound 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning and relevant examples. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 At the N ext Level, you’ll explore the various ways you can “ qualify” 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Issue statements, and you’ll learn how to develop an essay that accounts 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for “ pros” and “ cons” of both sides of an issue. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 80 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Explain How Your Examples Support Your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Viewpoint 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Anyone can simply list a long string of examples and claim that they 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 illustrate a point. But GM AT readers are looking for incisive analysis, not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fast typing. For each example you cite, be sure to tell the reader how it 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 supports the point you’re trying to make. O therwise, you argument will be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unconvincing, and your score might suffer as a result. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Appeal to Reason, Not Emotion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Avoid inflammatory statements, and don’t preach or proselytize. Ap2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 proach the Issue writing task as an intellectual exercise in which you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dispassionately argue for a certain viewpoint. Do not use it as a forum for 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sharing your personal belief system. It’s perfectly appropriate to criticize 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 particular behavior, policies, or viewpoints as operating against the best 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 interest of a business or of a society. But refrain from either condemning or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 extolling based on personal moral grounds. Also avoid demagoguery 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (appeal to prejudice or emotion) and jingoism (excessive patriotism). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Spare the Reader Rote Facts and Technical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Details 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The Issue essay is not like a game of Jeopardy! or Trivial Pursuit. You will 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 not score points simply by recounting statistics, compiling long lists, or 2 2 12345678901234567890123456789012123456789012345678901 conjuring up little-known facts. And, don’t try to impress the reader with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your technical knowledge of any particular subject. Resist the temptation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to use the Issue essay as a forum to recapitulate your senior-year thesis. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This is not the place to convince the reader of your firm grasp of the finest 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 points of foreign policy, macroeconomic theory, or market analysis. That’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what your GPA and undergraduate transcripts are for. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Avoid Obvious and Hackneyed Examples 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any GM AT test-takers will rely heavily on today’s headlines and on 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 history’s most illustrious and notorious figures. If you can, avoid relying 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 on these all-too-obvious examples. Try to dig a bit deeper, showing the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 reader a broader, more literate perspective. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ost GM AT readers reside in the United States. If you reside elsewhere, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cite examples from your own region of the world. You’re more likely to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 pique the reader’s interest, which can only operate in your favor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 81

Part II: A nalytical W riting A ssessm ent

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Dwell on One Point; But Don’t Try to Cover 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Everything, Either 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Avoid harping on one point you believe to be the most convincing one, or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on one example that you know a lot about or you feel best illustrates your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point. Instead, try to cover as many points in your outline as you have time 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 for, devoting no more than one paragraph to each one. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 At the same time, if you try to cover everything you can think of about the 2 2 12345678901234567890123456789012123456789012345678901 issue at hand, you’re likely to become frustrated, and you might even panic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as the testing clock ticks away your 30 minutes. The readers understand 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your time constraints. So don’t worry if you’re forced to leave the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 secondary and more tangential points on your scratch paper. Stick to your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outline, ration your time, and you’ll be fine. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Keep It Simple; the Reader Will Reward You for It 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Don’t make the Issue writing task more onerous than it needs to be for you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to attain a solid score. Keep your sentences clear and simple. Use a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 straightforward structure for your essay. Avoid using “ fancy” words just 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to impress the reader. Don’t waste time ruminating over how you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 come across as ultra-brilliant, mega-insightful, or super-eloquent. Finally, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 don’t waste brain-power or keystrokes trying to be clever, creative, or 2 2 12345678901234567890123456789012123456789012345678901 humorous. Be forewarned: Dazzling the reader with your amazing wit and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wisdom is not the way to score points. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Look Organized and in Control of the Task 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use every tool at your disposal to show the reader that you can write well 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 under pressure. Use logical paragraph breaks—one after your introduc- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 tion, one between each of your main points, and one before your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concluding paragraph. Be sure to present your main points in a logical, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 easy-to-follow sequence. (If you don’t get it right the first time, you can use 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the word processor’s cut-and-paste features to rearrange your ideas.) Your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay’s “ bookends” —the introductory and concluding paragraph—are 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 especially key to looking organized and in control. First of all, make sure 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 they’re there! Then, make sure they’re consistent with each other, and that 2 12345678901234567890123456789012123456789012345678901 2 2 they reveal your viewpoint and recap your reasons for your viewpoint. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 It’s Quality, Not Quantity, That Counts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The only limitation on your essay’s length is the practical one that the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 30-minute time limit imposes. But, do the readers prefer brief or longer 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Issue essays? Well, it all depends on the essay’s quality. A lengthy essay 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that’s articulate and that includes many insightful ideas that are well 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supported by examples will score higher than a briefer essay that lacks 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 substance. O n the other hand, an essay that’s concise and to the point can 2 2 12345678901234567890123456789012123456789012345678901 be more effective than a long-winded, rambling one. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Don’t worry about the word length of your essay. GM AT readers don’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 count words. As long as you incorporate into your essay all the suggested 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 elements you learned about in this lesson, you don’t need to worry about 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 length. Just keep in mind that it’s quality, not quantity, that counts. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Lose Sight of Your Primary Objectives 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The official scoring criteria for the Issue essay boil down to four broad 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 objectives. N ever lose sight of them during the 30-minute Issue section. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 After brainstorming and making notes, but before you start typing, ask 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Do I have a clear viewpoint on the issue? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Do I support my viewpoint with sound reasons and relevant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Do I have in mind a clear, logical structure for presenting my 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ideas? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nce you can confidently answer “ Yes” to each question, start composing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your essay. Then, once you’re finished your draft, ask yourself the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three questions again, as well as this fourth one: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. H ave I demonstrated good grammar, diction (word choice and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 usage), and syntax (sentence structure)? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O nce you can answer “ Yes” to all four questions, rest assured that you’ve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 produced a solid, high-scoring Issue essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 83

Part II: A nalytical W riting A ssessm ent

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument Analysis—Your 7-Step Game Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For a high-scoring Argument essay, you need to accomplish these four 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 basic tasks: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Identify and analyze the Argument’s key elements. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 2. O rganize, develop, and express your critique in a coherent and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 logically convincing manner. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Support your ideas with sound reasons and supporting examples. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Demonstrate adequate control of the elements of Standard 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Written English (grammar, syntax, and usage). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Just as for the Issue Analysis, you should spend some time up front 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 thinking about what you will write and how you will organize your ideas. 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Again, save some time at the end to proofread and fine-tune your essay. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere’s a 7-step game plan to help you budget your time so you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accomplish all four tasks listed above within your 30-minute time limit 2 2 12345678901234567890123456789012123456789012345678901 2 (suggested times are parenthesized): 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. Read the Argument, and identify its conclusions (1 min.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Examine the Argument’s evidence to determine how strongly it 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supports the Argument’s conclusion(s). (3 min.). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. O rganize and prioritize your points of critique (1 min.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Compose a brief introduction (2 min.). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. Compose the body of your response (16 min.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 6. Compose a concluding paragraph (2 min.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7. Proofread for significant mechanical problems (5 min.). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that, by following the suggested time limits for each step, you’ll 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spend about 5 minutes planning your essay, 20 minutes writing it, and 5 2 2 12345678901234567890123456789012123456789012345678901 minutes proofreading it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These time limits for each step are merely guidelines, not hard-and-fast 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 rules. As you practice composing your own Argument essays under timed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conditions, start with these guidelines, then adjust to a pace that works 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best for you. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 84 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the following pages, you’ll walk through each step in turn, applying the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following Argument statement, which is similar to some of the statements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the official pool: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Argument 1 (and directive) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following appeared in a memo from the manager of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 UpperCuts hair salon: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ According to a nationwide demographic study, more and more 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 people today are moving from suburbs to downtown areas. In 2 2 12345678901234567890123456789012123456789012345678901 order to boost sagging profits at UpperCuts, we should take 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 advantage of this trend by relocating the salon from its current 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 location in Apton’s suburban mall to downtown Apton, while 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 retaining the salon’s decidedly upscale ambiance. Besides, H air- 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dooz, our chief competitor at the mall, has just relocated 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 downtown and is thriving at its new location, and the most 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prosperous hair salon in nearby Brainard is located in that city’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 downtown area. By emulating the locations of these two successful 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 salons, UpperCuts is certain to attract more customers.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Discuss how well reasoned you find this argument. In your 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 discussion be sure to analyze the line of reasoning and the use of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 evidence in the argument. For example, you may need to consider 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 what questionable assumptions underlie the thinking and what 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 alternative explanations or counterexamples might weaken the 2 12345678901234567890123456789012123456789012345678901 conclusion. You can also discuss what sort of evidence would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strengthen or refute the argument, what changes in the argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would make it more logically sound, and what, if anything, would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 help you better evaluate its conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Read The Argument, and Identify Its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion(s) (1 Min.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Every GM AT Argument consists of the following basic elements: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Evidence (stated premises that the Argument does not dispute) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. A ssum ptions (unstated premises needed to justify a conclusion) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Conclusions (inferences drawn from evidence and assumptions) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you read an Argument for the first time, identify its final conclusion as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 well as its interm ediate conclusion (if any). Why is this first step so 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 important? Unless you are clear about the Argument’s conclusions, it’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 impossible to evaluate the author’s reasoning or the strength of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 85

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 evidence offered in support of them. And that’s what the Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 writing task is all about! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll probably find the final conclusion in the Argument’s first or last 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. The Argument might refer to it as a “ claim,” a “ recommenda2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion,” or a “ prediction.” An intermediate conclusion, upon which the final 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 conclusion depends, might appear anywhere in the Argument. N ot every 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument contains an intermediate conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Did you identify and distinguish between the intermediate and final 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusions in the Argument involving UpperCuts? H ere they are: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Interm ediate conclusion: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ By emulating the locations of these two successful salons, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 UpperCuts is certain to attract more customers.” 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Final conclusion: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ In order to boost sagging profits at UpperCuts, we should . . . 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 relocat[e] the salon from its current location in Apton’s suburban 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mall to downtown Apton, while retaining the salon’s decidedly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 upscale ambiance.” 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N otice that the Argument’s final conclusion relies on its intermediate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusions. H ere’s the essential line of reasoning: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 UC will gain customers if it moves downtown. (Interm ediate 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 T herefore, UC will boost its profits sim ply by moving downtown. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Final conclusion) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Always jot down an Argument’s intermediate conclusion (if any) and its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 final conclusion—in shorthand like we’ve provided above. You’ll need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refer to them time and again as you develop your points of critique and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compose your essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Identify and Examine the Argument’s Evidence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to Determine How Strongly It Supports the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument’s Conclusion(s) (3 Min.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 M ost Arguments contain at least two or three items of information, or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evidence, that are used in support of its conclusion(s). Identify them, label 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them, and jot them down in shorthand on your scratch paper. Argument 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contains three distinct items of evidence: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Evidence (item 1): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ According to a nationwide demographic study, more and more 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 people today are moving from suburbs to downtown areas.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Evidence (item 2): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 “ H air-Dooz, our chief competitor at the mall, has just relocated 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 downtown and is thriving at its new location.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Evidence (item 3): 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ . . . the most prosperous hair salon in nearby Brainard is located 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in that city’s downtown area.” 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext, analyze each item as to how much support it lends to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument’s intermediate and final conclusions. For the most part, what 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you should look for are any unsubstantiated or unreasonable assum ptions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 upon which the Argument’s conclusions depend. For example, an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Argument might rely on one of these assumptions, yet fail to provide 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evidence to support it. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • An event that occurs after another was caused by the other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (a false-cause problem). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Two things that are similar in one way are similar in other ways 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (a false-analogy problem). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statistical sample of a group is representative of the group as a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whole. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also check for problems with the Argument’s internal logic (for example, 2 12345678901234567890123456789012123456789012345678901 self-contradictions or circular reasoning). These types of problems don’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occur commonly in GM AT Arguments; but you should be on the lookout 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for them, anyway. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Just as for your Issue essay, don’t filter your ideas during this crucial 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 brainstorming step! Let them all flow onto your scratch paper. (You’ll sort 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them out in step 3.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Without exception, each Argument in the official pool contains at least 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three or four discrete assumptions or other problems—that’s how the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 test-makers design them. When you Tak e It to the N ex t L evel, you’ll 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examine in detail the most common flaws in GM AT Arguments. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 87

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Below is an example of what a test-taker’s notes for Argument 1 might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 look like after a few minutes of brainstorming: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inter. concl.—UC will gain customers downtown 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 final concl.—UC will improve profits downtown 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 demog. study—is Apton typical? no trend 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 reverse trend 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 success of HD—is location key? marketing 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 key stylist 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 success of B salon—downtown location key? 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 —is Apton like Brainard? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (demog.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 other problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 —relocation expenses offset revenues 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 —UC must establish new clientele 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 —competition from HD 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (suff. demand for both salons?) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 —demand for “upscale” salon downtown? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Organize and Prioritize Your Points of Critique 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1 Min.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Using your notes from step 2 as a guide, arrange your ideas into 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraphs (probably three or four, depending on the number of problems 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 built into the Argument). Take a minute to consider whether any of the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 flaws you identified overlap and whether any can be separated into two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 distinct problems. In many cases, the best sequence in which to organize 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your points of critique is the same order in which reasoning problems arise 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the Argument. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Just as you would for your Issue essay, try to use your notes as an outline, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbering points according to their logical sequence. The next page 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shows an example of what the test-taker’s notes for Argument 1 look like 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 after organizing them (arrows indicate where he intend to discuss a point; 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ [FC]” refers to final conclusion): 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inter. concl. UC will gain customers downtown 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 final concl. UC will improve profits downtown 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 no trend 2 12345678901234567890123456789012123456789012345678901 1 demog. study is Apton typical? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reverse 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 trend 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 marketing 2 12345678901234567890123456789012123456789012345678901 2 1 2345678901234567890123456789012123456789012345678901 2 1 success of HD is location key? 2 12345678901234567890123456789012123456789012345678901 key stylist 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 1 success of B salon downtown location key? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 is Apton like Brainard? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (demog.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 1 [FC] relocation expenses offset revenues 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 UC must establish new clientele 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 competition from HD 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (suff. demand for both salons?) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 demand for upscale salon downtown? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Compose a Brief Introductory Paragraph (2 Min.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you’ve spent about five minutes planning your essay, its time to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compose it. Don’t waste time repeating the quoted Argument; the reader, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whom you can assume is already well familiar with the Argument, is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interested in your critique—not in your transcription skills. H ere’s what 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you should try to accomplish in your initial paragraph: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the Argument’s final conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. D escribe briefly the Argument’s line of reasoning and evidence in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 support of its conclusion. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. A llude generally to the problems with the Argument’s line of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning and use of evidence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can probably accomplish all three task in 2–3 sentences. H ere’s a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise introductory paragraph of a response to Argument 1: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Citing a general demographic trend and certain evidence about two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other hair salons, the manager of UpperCuts (UC) concludes here that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 UC should relocate from suburban to downtown Apton in order to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 attract more customers and, in turn, improve its profitability. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 89

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H owever, the manager’s argument relies on a series of unproven 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions and is therefore unconvincing as it stands. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your introductory paragraph is the least important component of your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay. So, you might consider waiting until you’ve completed your critique 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the Argument before composing your introduction. If you’re running 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 out of time for your introduction, begin your essay with a sentence like one 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the following two, then delve right into your first point of critique— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without a paragraph break: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 This argument suffers from numerous flaws which, considered 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 together, render untenable the conclusion that UpperCuts should 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 relocate to downtown Apton. O ne such flaw involves . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 I find the argument for moving UpperCuts salon downtown specious 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 at best, because it relies on a series of unproven and doubtful 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions. O ne such assumption is that . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. Compose the Body of Your Response (16 Min.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 As in the Issue essay, your chief aim during this step is to peck madly at 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your keyboard in order to get your ideas onto the screen! H ere’s what you 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 need to keep in mind as you compose your body paragraphs: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Try to devote a separate paragraph to each major point of your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 critique—but be flexible. Sometimes it makes more sense to discuss 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 related points in the same paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Be sure the first sentence of each paragraph conveys to the reader 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the essence of the problem you’re dealing with in that paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • For each of the Argument’s assumptions, try to provide at least 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one example or counterexample (a hypothetical scenario) that, if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 true, would undermine the assumption. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Try to devote no more than three or four sentences to any one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point in your outline. O therwise, you risk running out of time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without discussing all of the Argument’s major problems. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Arrange your paragraphs so that your essay flows logically from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one point of critique to the next. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Don’t worry if you don’t have time to discuss each and every point 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of critique or example that you noted during step 2. The readers 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 understand your time constraint. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Try to stick to your outline, but be flexible. Start with whichever points of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 critique strike you as the most important, are clearest in your mind, and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 are easiest to articulate. (You can always rearrange your points later, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during step 6, using the word processor’s cut-and-paste feature.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 H ere’s the body of a test-taker’s response to Argument 1. As you read 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 these four paragraphs, notice that each paragraph addresses a distinct, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 critical assumption—a certain condition that must be true to justify one of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the Argument’s conclusions. Also notice that each paragraph describes at 2 2 12345678901234567890123456789012123456789012345678901 least one scenario that, if true, would serve to undermine an assumption. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 O ne such assumption is that Apton reflects the cited demographic 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trend. The mere fact that one hair salon has moved downtown hardly 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suffices to show that the national trend applies to Apton specifically. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For all we know, in Apton there is no such trend, or perhaps the trend 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 is in the opposite direction, in which event the manager’s recommen- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dation would amount to especially poor advice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Even assuming that downtown Apton is attracting more residents, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 relocating downtown might not result in more customers for UC, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 especially if downtown residents are not interested in UC’s upscale 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 style and prices. Besides, H air-Dooz might draw potential customers 2 2 12345678901234567890123456789012123456789012345678901 away from UC, just as it might have at the mall. Without ruling out 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these and other reasons why UC might not benefit from the trend, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 manager can’t convince me that UC would attract more customers by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 moving downtown. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Even if there was a high demand for UC’s service in downtown Apton, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an increase in the number of patrons would not necessarily improve 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 UC’s profitability. UC’s expenses might be higher downtown, in which 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 case it might be no more, or perhaps even less, profitable downtown 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than at the mall. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 As for the Brainard salon, its success might be due to particular factors 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that don’t apply to UC. For example, perhaps the Brainard salon 2 12345678901234567890123456789012123456789012345678901 thrives only because it is long-established in downtown Brainard. O r 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perhaps hair salons generally fare better in downtown Brainard than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 downtown Apton, due to demographic differences between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 areas. In short, the manager simply cannot justify his proposal on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basis of the Brainard salon’s success. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 91

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 6. Compose a Concluding Paragraph (2 Min.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Unless your essay has a clear ending, the reader might think you didn’t 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 finish on time; so be sure to make time for a final paragraph that clearly 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ wraps up” your essay. Your final paragraph is not the place to introduce 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 any new points of critique. Instead, recapitulate the Argument’s problems— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 e.g., a series of unproven assumptions—in two or three sentences. H ere’s a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 final paragraph in response to Argument 1: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In sum, the argument relies on what might amount to two poor 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 analogies between UC and two other salons, as well as a sweeping 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 generalization about demographic trends, which may or may not 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 apply to Apton. Thus, even though the manager has provided some 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scant evidence to support the recommendation, on balance I find the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument unconvincing at best. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that this paragraph does not introduce any new points of critique. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 It’s just a brief recap of the argument’s major problems, along with a 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 reiteration of why the Argument is weak. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Another tack for your concluding paragraph is to recap in terms of how 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the argument could be strengthened and/or how additional information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might be needed to evaluate it. Although these two elements are optional, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorporating one or both into your essay can boost your score. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 From beginning to end (including the introductory, body, and concluding 2 2 12345678901234567890123456789012123456789012345678901 paragraphs), the preceding sample essay runs just under 400 words in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 length—brief enough to plan and write in 30 minutes. It’s well organized; 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it articulates the Argument’s major problems; it supports each point of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 critique with relevant examples; and it’s crisp, clear, and convincing. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 short, it contains all the elements of a high-scoring GM AT Argument essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7. Review for Coherence and Proofread for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Significant Mechanical Problems (5 Min.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Be sure to reserve time to check the flow of your essay, paying particular 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 attention to the first sentence of each paragraph. Check to see if you should 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rearrange paragraphs so that they appear in a more logical sequence. Also, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 proofread for glaring mechanical problems. Your Argument essay, like your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Issue essay, need not be flawless in order to earn a high score. The readers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t mark you down for the occasional awkward sentence and minor 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 error in punctuation, spelling, grammar, or diction (word choice and us- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 age). Use whatever time remains to fix the most glaring mechanical prob- 2 2 12345678901234567890123456789012123456789012345678901 lems. Correct spelling and punctuation errors only when they’re likely to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 interfere with the reader’s understanding of the point at hand. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for Writing a GMAT Argument2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis Essay 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the following pages, we’ve distilled our very best advice for GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument-Analysis down to bite-sized nuggets that you can easily digest. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any of them reiterate suggestions we’ve already made—suggestions that 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 are well worth underscoring. O thers are new here. Apply these points of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 advice to Part III’s practice tests, and then review them again just before 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exam day. You’ll be glad you did! 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Ferreting Out the Flaws Is Half the Battle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Built into each and every GM AT Argument are at least three or four 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 distinct reasoning problems. That’s how the test-makers design them. To 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 earn a high score, first and foremost, your essay must identify these 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 problems. After brainstorming and making notes, if you haven’t isolated at 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 least three major flaws, then you can be sure that you’ve missed at least 2 12345678901234567890123456789012123456789012345678901 one. Read the Argument again—very carefully. (Even a few overlooked 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 words can be key.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Ration your time to be sure the reader knows you’ve recognized each and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 every problem listed in your notes. Don’t worry if 30 minutes isn’t enough 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 time for you to discuss each problem in detail. When it comes to analyzing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Arguments, remember that breadth is better than depth. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Arguments are not all created equal. Some are flawed in more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ways than others. The greater the number of distinct flaws, the more 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 forgiving the reader will be. So if an Argument contains as many as five or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 six distinct problems, and you overlook one or two of them, you can still 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 attain a high score—perhaps even a top score of 6 assuming your essay is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outstanding in all other respects. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Viewpoints and Opinions Don’t Matter—At All 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In sharp contrast to the Issue essay, your Argument essay is not the place to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 present viewpoints or opinions about an issue that the Argument might 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 touch up on. Your analysis must focus strictly on the Argument’s logical 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 features and on how strongly its evidence supports its conclusions. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For instance, consider an Argument for electing a certain political 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 candidate because she has a record of being tough on crime. In an Issue 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 essay involving the problem of violent crime, it would be perfectly 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 appropriate to present various viewpoints on this social issue—weighing 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 alternative approaches to the problem in general. But these viewpoints are 2 12345678901234567890123456789012123456789012345678901 irrelevant to the Argument writing task. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 93

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Leave Any Point of Critique Without Support 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t neglect to support each point of your critique with at least one 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example or counterexample that helps the reader understand the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 particular flaw you’re pointing out. Keep your examples and counter- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 examples hypothetical (“ What if . . . ,” “ Suppose that . . . ,” or It’s possible 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that . . .” or “ Perhaps . . .” ) You don’t need to go into great detail; one or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two for each point of critique will suffice. Unless you provide some 2 2 12345678901234567890123456789012123456789012345678901 support for each point of critique, your score might suffer. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 But what if you think you won’t have enough time to provide supporting 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 detail for each and every point of critique in your notes? Don’t despair. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Look for two or three points that are related to the same item of evidence 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (for example, points that all involve the same statistical survey). Then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plan to touch briefly on each one in the sam e paragraph. Grouping them 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 together this way will make sense to the reader, who might not notice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what’s missing as much as the fact that you’re very organized! 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Look for the “Fatal Flaw”; Instead, Treat 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Every Problem as a Contributing Cause of Death 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Avoid dwelling on one particular flaw that you think is the most serious 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one—or on one realistic example or counterexample that you think, if true, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 would spell certain death for the entire Argument. O therwise, you risk 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 running out of time to identify all the problems you’ve listed in your notes. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, don’t try to rank any flaw as “ more serious” or “ less serious” than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another. True, one particular flaw might be more damaging to an 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Argument than others. But by identifying it as “ the most serious problem 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with the Argument,” you’re committing yourself to defend this claim, by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weighing that problem against all the others. Do you really have time for 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this kind of analysis? N o! N or do the GM AT readers expect or want this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from you. In short, you’re best off applying equal treatment to each of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument’s problems. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 There’s No Need to Impress with Technical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Terminology 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Scholars in the academic fields of Critical Reasoning and Logic rely on all 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sorts of formal terminology (much of which comes from the Latin 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 language), for the kinds of reasoning flaws that you’ll find in GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Arguments. For example, post hoc reasoning refers to faulty “ After this, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 therefore because of this” reasoning. But you won’t score any points with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT readers by tossing around such terminology in your Argument 2 2 12345678901234567890123456789012123456789012345678901 essay. Besides, if you refer a technical term, you’ll then need to define it for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 the reader, which will only consume your precious time. So don’t bother! 2 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Go with the Logical Flow 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Try to organize your points of critique to reflect the Argument’s line of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning—from its evidence and assumptions to its intermediate conclu- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sion (if any), then to its final conclusion. Fortunately, most GM AT 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Arguments are already organized this way—so that your points of critique 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 can simply follow the quoted Argument from beginning to end. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But don’t assume that this sequence will be the most logical one. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Regardless of the sequence of ideas in the quoted Argument, try to group 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 together all your points of critique that involve the same item of evidence 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (for example, a statistical survey or study). Also, it makes logical sense to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 address problems involving the Argument’s intermediate conclusion 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 before those involving its final conclusion. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look Organized and in Control 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 As with the Issue essay, use every means at your disposal to show that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reader that, even under significant time pressure, you know how to 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 organize your ideas and convey them in writing. Use logical paragraph 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 breaks, present your points of critique in a logical sequence, and try to save 2 2 12345678901234567890123456789012123456789012345678901 time for brief introductory and concluding paragraphs. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Lose Sight of Your Primary Objectives 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The official scoring criteria for the Argument essay boil down to four 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 broad objectives. N ever lose sight of them during your 30-minute 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument section. After brainstorming and making notes, but before you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 start typing, ask yourself: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. H ave I clearly identified each of the Argument’s major problems? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Can I support each point of my critique with at least one relevant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example or counter-example? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Do I have in mind a clear, logical structure for presenting my 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points of critique? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O nce you can confidently answer “ Yes” to each question, start composing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your essay. Then, once you’re finished your draft, ask yourself the same 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three questions, as well as this fourth one: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. H ave I demonstrated good grammar, diction (word choice and 2 12345678901234567890123456789012123456789012345678901 usage), and syntax (sentence structure)? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O nce you can answer “ Yes” to all four questions, rest assured that you’ve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 produced a solid, high-scoring Argument essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 95

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Writing Style and Mechanics 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The testing service instructs GM AT readers to place less weight on writing 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 style and mechanics than on content and organization. But, this doesn’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mean that the first two factors won’t influence the reader or affect your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analytical Writing Assessment score. Indeed, they might! If the way you 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 write interferes with the reader’s understanding of your ideas, then be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prepared for a disappointing score. And, in any event, poor writing will 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 predispose the reader to award a lower score, regardless of your ideas or 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 how you organize them. To ensure yourself a high Analytical Writing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Assessment score, strive for writing that is: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Appropriate in tone and “ voice” for graduate-level, academic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 writing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Varied in sentence length and structure (to add interest and variety 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as well as to demonstrate maturity and sophistication in writing 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 style) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Clear and concise (easy to follow and direct rather than wordy or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 verbose) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Correct in grammar, mechanics, and usage (conforming to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 requirements of Standard Written English) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Persuasive in style (using rhetorical devices effectively) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 All of this is easier said than done, of course. Don’t worry if you’re not a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 natural when it comes to writing effective prose. You can improve your 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 writing for your exam, even if your time is short. Start by reading the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suggestions and guidelines in the following pages. But, keep in mind: 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 improvement in writing comes mainly with practice. So you’ll also need to 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 apply what you learn here to the practice tests in Part III of this book. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This section covers all writing aspects listed above except grammar and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 persuasiveness (the last item). The rules of grammar you reviewed in the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Sentence Correction lessons of this book are the same ones you should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 keep in mind as you compose and proofread your essays. And, if you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 advance to the N ext Level that’s where you’ll pick up ideas for developing 2 2 12345678901234567890123456789012123456789012345678901 a persuasive writing style. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Overall Tone and Voice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In general, you should try to maintain a somewhat formal tone throughout 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both your essays. An essay that comes across as conversational is probably 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 a bit too informal for the GM AT. H ere’s a brief list of additional 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 guidelines: 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 96 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. The overall tone should be critical, but not inflammatory or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 emotional. Don’t try to overstate your position by using extreme 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or harsh language. Don’t attempt to elicit a visceral or emotional 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 response from the reader. Appeal instead to the reader’s intellect. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. When it comes to your main points, a very direct, even forceful 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 voice is perfectly acceptable. But don’t overdo it; when it comes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the details, use a more dispassionate approach. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 3. Don’t try to make your point with “ cutesy” or humorous 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 remarks. Avoid puns, double-meanings, plays on words, and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other forms of humor. N ot that GM AT readers don’t have a sense 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 of humor; it’s just that they leave it at the door when they go to 2 2 12345678901234567890123456789012123456789012345678901 work for ETS. (That sentence exhibits just the sort of “ humor” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you should avoid in your essays.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Sarcasm is entirely inappropriate for your GM AT essays. Besides, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the reader might not realize that you’re being sarcastic, in which 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 case your remark will only serve to confuse the reader. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence Length and Variety 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To ensure a high Analytical Writing Assessment score, strive for sentences 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that are varied in length and structured in a manner that helps convey their 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 intended meaning, rather than obscuring or distorting it. H ere are some 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 specific warnings and suggestions: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Sentences that vary in length make for a more interesting and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 persuasive essay. For rhetorical emphasis, try using an abrupt short 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sentence for a crucial point, either before or after longer sentences 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that elucidate that point. For additional variety, use a semicolon to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 transform two sentences involving the same train of thought into 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one; and use the word “ and” to connect your two independent 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clauses (just as in this sentence). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Sentences that use the same essential structure can help convey 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your line of reasoning to the reader. Try using the same structure 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 for a list of reasons or examples. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Sentences that essentially repeat (verbatim) throughout your essay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggest an immature, unsophisticated writing style. Try to avoid 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using so-called “ template” sentences over and over—especially for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the first (or last) sentence of each body paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 97

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To speed up the writing process, some GM AT test-takers copy and paste 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain phrases and sentences, then “ tweak” them to avoid the template 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 look. There’s nothing wrong per se with this strategy. But you’ll probably 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 find that it takes more time than it’s worth. You’re better off composing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each sentence from scratch. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Clear and Concise Writing 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 You’re more likely to score high on your GM AT essays with writing that is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear and concise. Frequent occurrences of awkward, wordy, or redundant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrases can lower your Analytical Writing Assessment score by a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 notch—especially if these problems interfere with the reader’s understand2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ing of your essay. And, although punctuation is the least important aspect 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of your GM AT essays, the habitual overuse, underuse, or misuse of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 commas can also contribute to lowering your score. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Wordy and awkward phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 With enough words, anyone can make the point; but it requires skill and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effort to make your point with concise phrases. As you proofread your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay, if a sentence seems clumsy or too long, check for a wordy, awkward 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrase that you can replace with a clearer, more concise one. H ere are two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples (replace italicize phrases with the ones in parentheses): 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Discipline is crucial to the attainm ent of one’s objectives. (attain) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To indicate the fact that they are in opposition to a bill, legislators 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sometimes engage in filibusters. (To show their) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for the opportunity to change prepositional phrases into one-word 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 modifiers: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The employee w ith am bition . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The am bitious employee . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can often rework clauses with relative pronouns (that, w ho, w hich, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 etc.), omitting the pronoun: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The system, w hich is most efficient and accurate . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The most efficient and accurate system . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In your Argument essay, you can replace wordy phrases that signal a 2 2 12345678901234567890123456789012123456789012345678901 premise with a single word: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Wordier: the reason for, for the reason that, due to the fact that, in light 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the fact that, on the grounds that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 More concise: because, since, considering that 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Redundant words and phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you proofread your essays, check for words and phrases that express 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the same essential idea twice. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Both unemployment levels as w ell as interest rates can affect stock 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prices. (Replace as w ell as with and, or omit both.) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 T he reason science is being blamed for threats to the natural 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 environment is because scientists fail to see that technology is only as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 useful, or as harmful, as those who decide how to use it. (Replace 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because with that, or omit the reason and is.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Using too few (or too many) commas 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although punctuation is the least important aspect of your GM AT essays, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 too few or too many commas might interfere with the reader’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 understanding of a sentence. Too few commas might confuse the reader, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 while too many can unduly interrupt the sentence’s flow. H ere’s the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 guideline: Use the minimum number of commas needed to ensure that the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reader will understand your point. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your Facility with the English Language 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To ensure yourself top scores on your essays, strive to convince the readers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that you possess a strong command of the English language—in other 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 words, that you can use the language correctly, clearly, and persuasively in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 writing. To show the reader the requisite linguistic prowess, try to: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Demonstrate a solid vocabulary. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Use proper idioms (especially prepositional phrases). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 • Use proper diction (word usage and choice). 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Demonstrating a solid vocabulary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 By all means, show the reader that you possess the vocabulary of a broadly 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 educated individual, and that you know how to use it. But keep the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following caveats in mind: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Don’t overuse SAT-style words just to make an impression. Doing 2 12345678901234567890123456789012123456789012345678901 so will only serve to warn the reader that you’re trying to mask 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 poor content with window dressing. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Avoid obscure or archaic words that few readers are likely to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know. The readers will not take time while reading essays to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 consult their unabridged dictionaries. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 99

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Avoid technical terminology that only specialists and scholars in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 specific field understand. GM AT readers are typically English2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 language generalists from the academic fields of English and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Communications, not economic-policy analysts. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Use Latin and other non-English terms very sparingly. After all, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 one of the primary skills being tested through the GM AT essays is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your facility with the English language. H owever, the occasional 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use of Latin terms and acronyms—for example, per se, de facto, ad 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 hoc, and especially i.e., and e.g.,—are perfectly acceptable. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N on-English words used commonly in academic writing—such as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 vis-à-vis, caveat, and laissez faire—are acceptable as well. Again, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just don’t overdo it. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The rules for Standard Written English require that Latin and other 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 non-English terms be italicized (or underlined). H owever, the GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 word processor does not allow you to incorporate these attributes or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 special diacritical marks (as in vis-à-vis). So leave words such as these as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is, but be sure they are terms that most educated people are familiar with. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Avoid colloquialisms (slang and vernacular). O therwise, instead of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hitting a home run with your essay, your essay will turn out lousy, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and you’ll be out of luck and need to snake your way into a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bottom-barrel B-school. (Did you catch the five colloquialisms in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the preceding sentence?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Your diction and use of idioms 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In evaluating your essays, GM AT readers also take into account your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 diction and use of idiom s—again, especially when problems in these areas 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 interfere with the readers’ understanding of your essays. H ere you’ll learn 2 2 12345678901234567890123456789012123456789012345678901 tips for avoiding, or at least minimizing, diction and idiom errors in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your essays. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Diction (word choice and usage) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D iction refers to word choice as well as to the manner in which a word is 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 used. For instance, you might confuse one word with another because the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two words look or sound similar. O r you may choose a word that doesn’t 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 accurately convey your idea. H ere’s an example of each type of diction error: 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 One type of diction error: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The best way to im pede employees to improve their productivity is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to allow them to determine for themselves the most efficient way of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 performing their individual job tasks. 2 1 2 100 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (The word im pede means “ to hinder or hamper” ; in the context of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this sentence im pede should be replaced with a word such as im pel, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which means “ propel or drive.” The test-taker might have 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 confused these two words.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Another type of diction error: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Unless the department can supply a comparative cost-benefit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 analysis for the two alternative courses of action, I would remain 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 diffident about following the department’s recommendation. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (The word diffident means “ reluctant, unwilling, or shy.” A more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appropriate word here would be am bivalent, which means 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ undecided or indecisive.” O r perhaps the test-taker meant to use 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the word indifferent (thereby committing the first type of diction 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 error). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 What appear to be diction errors might in many instances be mere clerical 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (typing) errors. Accordingly, problems with your word choice and usage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will adversely affect your scores only if they are obvious and occur 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 frequently. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Idiom 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 An idiom is a distinctive (idiosyncratic) phrase that is considered proper or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 improper based upon whether it has become acceptable over time— 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 through repeated and common use. H ere are two sentences, each of which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contain an idiomatic prepositional phrase as well as another idiom. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Example (from a typical Issue essay): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The speaker’s contention flies in the face of the empirical evidence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and, in any event, runs contrary to common sense. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Example (from a typical Argument essay): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For all w e k now , last year was the only year in which the company 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 earned a profit, in which case the vice president’s advice might turn 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 out especially poor in retrospect. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Tips for avoiding diction and idiom errors 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Idioms don’t rely on any particular rules of grammar; hence, they are 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 learned over time by experience. As you might suspect, the English 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 language contains more idiomatic expressions than you can shake a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 thesaurus at. M oreover, the number of possible diction errors isn’t even 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 limited to the number of entries in a comprehensive unabridged English 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 dictionary. Although it is impossible in these pages to provide an adequate 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 101

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 diction or idiom review, here are some guidelines to keep you on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 straight and narrow when it comes to these aspects of your writing. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If you’re the least bit unsure about the meaning of a word you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 intend to use in your essay, don’t use it. Why risk committing a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 diction blunder just to impress the reader with an erudite vocabu12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 lary? (And if you’re not sure what “ erudite” means, either find out 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or don’t use it in your essays!) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • If a phrase sounds wrong to your ear, change it until it sounds 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct to you. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The fewer words you use, the less likely you’ll commit an error in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 diction or idiom. So when in doubt, go with a relatively brief 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrase that you still think conveys your point. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If English is your second language, take heart: In evaluating and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scoring your essays, GM AT readers take into account diction or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 idiom problems only to the extent that those problems interfere 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with a reader’s understanding of your sentence’s intended mean12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ing. So as long as your writing is understandable to your EFL 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (English-as-first-language) friends, you don’t need to worry. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you have ample time before your exam, and you think your diction and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use of idioms could stand considerable improvement, check for errors in 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your practice essays by consulting a reputable guide to English usage—or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 a trusted professor, colleague, or acquaintance who has a firm grasp of 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the conventions of Standard Written English. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 102 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level of Analytical Writing Assessment. At this level, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you’ll learn advanced skills and techniques that will help you attain not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only a solid Analytical Writing Assessment score, but no less than a top 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 score of 6. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the Issue-Analysis writing task, at the N ext Level you’ll learn to: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Recognize and deal with the kinds of complexities inherent in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Issues but that many test-takers overlook. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Acknowledge and respond effectively to ostensible weaknesses of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your viewpoint on an Issue. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Acknowledge and respond effectively to the merits of viewpoints 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that are contrary to yours. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For the Argument-Analysis writing task, at the N ext Level you’ll learn to: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Recognize each of the typical types of flaws you’ll find in GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Arguments. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Compose a concise and effective one-paragraph analysis of each 2 12345678901234567890123456789012123456789012345678901 type of flaw. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Incorporate optional elements into your essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll also learn to develop an especially mature 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and persuasive writing style—one that will leave a distinctively positive 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 impression on any GM AT reader. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—“Qualifying” Your Viewpoint 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ost GM AT test-takers will essentially accept (agree with) or reject 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (disagree with) the Issue statement that the test presents to them. And 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 that’s okay. As long as you provide sound reasons and relevant examples 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 103

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 in support of your position, you’ll earn a solid score on your essay. But 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re more likely to receive a top score of 6 if you demonstrate additional 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 insight into the issue at hand. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 O ne way to accomplish this is to think of ways that you can qualify the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement—or your viewpoint on it. What this means is that you agree (or 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 disagree) with the statement only in part or to a certain extent. In other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 words, you neither completely agree nor completely disagree with the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement. H ere are two Issue statements, which are typical of the ones in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the official pool, each followed by a viewpoint that expresses how the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test-taker might qualify it: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Issue Statement 1: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ To truly succeed in life, a person must assert his or her 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 individuality rather than conforming to the expectations of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 others.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 View point: Asserting individuality is important only to an extent. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 key is to strike the optimal balance between individuality and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conformity—a balance that varies depending on the particular activity 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or goal involved. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Issue Statement 2: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The greatest responsibility of a leader—whether in politics, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 business, or the military—is to serve the interests of his or her 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 followers.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 View point: The statement’s accuracy depends on the category. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Legitimate political leadership must, by definition, serve the citizenry, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but the same can’t be said for either business or military leadership. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You might be wondering: By qualifying the statement, wouldn’t I appear 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 wishy-washy or indecisive? To the contrary! By “ hedging your position” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the Issue, you’ll impress the reader as thoughtful and insightful! Just be 2 2 12345678901234567890123456789012123456789012345678901 sure to persuade the reader (with sound reasons and relevant examples) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that your qualified agreement (or disagreement) is justifiable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n your exam, look especially for any of the following types of qualifiable 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue statements: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A statement whose accuracy depends on various factors 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A statement that might be generally true (or untrue) but that fails 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to account for significant exceptional cases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that is unclear or vague in some way (in other words, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the statement’s accuracy depends on the meaning of key terms or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 how you interpret the statement as a whole) 2 1 2 104 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A statement that raises two distinct but related issues (one might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be a threshold issue, which the statement ignores but that should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be addressed before analyzing the main issue) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • A statement that has merit but overlooks legitimate competing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interests or contributing factors—e.g., Issue Statement 1 above 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • A statement that lists, or otherwise embraces, two or more distinct 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 categories—e.g., Issue Statement 2 above (different categories 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 often lend differing degrees of support to the statement) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you have time before exam day, select one or two dozen Issue 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 statements from the official pool. Try to qualify each one using the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 preceding list to help you brainstorm ideas. Jot down your viewpoint in 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one or two sentences that could serve as an introduction to an essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—Debating a Statement’s 2 12345678901234567890123456789012123456789012345678901 2 1 “Pros” and “Cons” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Earlier in the chapter, we suggested that you take a few minutes up front to 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 brainstorm and jot down ideas, listing points both for and against the 2 12345678901234567890123456789012123456789012345678901 statement as you think of them. As an advanced test-taker, you should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 think more consciously about “ pros” and “ cons” during this step. Think 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of this process as a debate, in which you formulate points and supporting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples to bolster one side of the issue. Then respond with counterpoints 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and counterex am ples. (You can even go a step further, to rebut a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 counterpoint or counterexample.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To organize the points of your debate, try creating two columns, one for 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 points that support the statement (the “ pro” column) and the other for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opposing points (the “ con” column). To help you see how this might work, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 here’s what a test-taker’s notes might look like after a few minutes of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 brainstorming “ pros” and “ cons” of Issue Statement 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Issue Statement 3: 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The best way to ensure protection and preservation of our natural 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 environment is through government regulatory measures. We 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cannot rely on the voluntary efforts of individuals and private 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 businesses to achieve these objectives.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 105

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 PRO CON 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 lawmakers pander self-interest rules ind. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but accountable to & bus. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 voters e.g. auto emissions 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nations too but enforcement problems 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 e.g. bus. relocate environ problems too wide2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spread for ind. & bus. 2 12345678901234567890123456789012123456789012345678901 bureaucratic problems 2 12345678901234567890123456789012123456789012345678901 but nations must coop2345678901234567890123456789012123456789012345678901 2 1 e.g. delays 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 erate 2 12345678901234567890123456789012123456789012345678901 e.g. compromises 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 e.g. admin. expense 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but must put up with 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 problems to save 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 environ. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that the test-taker supports each main point (indicated by a bullet) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with one or more examples (“ e.g.” ) and/or a counterpoint (“ but” ). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t worry if you don’t quite understand what each of the preceding 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 notes means. You’ll find out what the test-taker had in mind as you a read 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 complete essay based on these notes later in this chapter. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—Developing Rhetorical 2 12345678901234567890123456789012123456789012345678901 2 1 Arguments 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The word “ rhetoric” refers to the art of persuasive argumentation. A 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rhetorically effective Issue essay does more than just itemize the best 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasons and examples in support of one viewpoint on the issue. It also: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Acknowledges possible problems with the writer’s viewpoint, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 defends that viewpoint by responding to those problems head-on 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Acknowledges at least one other position or viewpoint, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 challenges that viewpoint directly 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H opefully, as you take notes on your Issue statement, ideas for responding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to (or “ countering” ) other viewpoints, and to possible problems with your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 own viewpoint will occur to you naturally. But if you do get stuck for 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 106 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ideas, draw upon the five tried-and-true techniques discussed in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following pages to get your rhetorical ideas flowing. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To illustrate each technique, we’ll use examples based upon the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two Issue statements, the first of which you’ve already encountered in this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lesson: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Issue Statement 3: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ The best way to ensure protection and preservation of our natural 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 environment is through government regulatory measures. We 2 2 12345678901234567890123456789012123456789012345678901 cannot rely on the voluntary efforts of individuals and private 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 businesses to achieve these objectives.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue Statement 4: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ Large businesses should focus on teamwork as the primary means 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of achieving success.” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Turn it Around (Look for the “Silver Lining”) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argue that an apparent weakness (or strength) is actually not, or perhaps 2 12345678901234567890123456789012123456789012345678901 even just the opposite, if you view it from a different perspective. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 notes/outline for Issue Statement 3 provide a good example. The writer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might first cite evidence that lends apparent support to the opposing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Admittedly, businesses often attempt to avoid compliance by conceal- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ing their activities, or calculate the cost of polluting, in terms of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 punishment, then budget in advance for anticipated penalties and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 openly violate the law. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Then the writer might indicate how this point actually undermines that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 . . . H owever, this behavior only serves to underscore the need for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 government intervention, because, left unfettered, this type of behavior 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would only exacerbate environmental problems. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Trivialize it (“Explain it Away”) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Argue that an apparent weakness of your position (or strength of a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 different position) is trivial, minor, or insignificant. Issue Statement 4 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 provides a good opportunity to use this technique. The writer might first 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 cite two examples that lend apparent support to those who might disagree 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with the statement: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 107

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Detractors might cite the heavy manufacturing and natural-resource 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 industries, where the value of tangible assets—raw materials and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 capital equipment—are often the most significant determinant of 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 business success. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then the writer might ex plain aw ay these examples. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 . . . H owever, such industries are diminishing in significance as we 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 move from an industrial society to an information age. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Appeal to Broader Considerations 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Argue that any minor problems with your position seem trivial in light of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the broad, and serious, implications that the Issue raises. The notes/outline 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for Issue Statement 3 provide a good example. The writer might first 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 acknowledge a certain problem with her position. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Delays typically associated with bureaucratic regulation can thwart 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the purpose of the regulations, because environmental problems can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quickly become grave indeed. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then the writer might point out the broad societal consideration that puts 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this minor drawback in its proper perspective. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 . . . But such delays seem trivial when we consider that many 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 environmental problems carry not only a real threat to public health 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but also a potential threat to the very survival of the human species. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The “Lesser of Two Evils” Method 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argue that an opposing position is not stronger, but perhaps even weaker, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in a certain respect. The notes/outline for Issue Statement 1 provides a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 good example. The writer might first acknowledge a certain weakness in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 his position. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Delays typically associated with bureaucratic regulation can thwart 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the purpose of the regulations, because environmental problems can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quickly become grave indeed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, the writer would point out an even greater weakness in the opposing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 . . . H owever, given that unjustifiable reliance on volunteerism is the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only alternative, government regulation seems necessary. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 108 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The “Greater of Two Virtues” Method 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argue that a certain merit of the opposing position is overshadowed by 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one or more virtues of your position. Issue Statement 4 provides a good 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 opportunity to employ this rhetorical device. The writer might first admit 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the opposing position is not without merit. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 N o reasonable observer of the corporate business world could disagree 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the leadership and vision of a company’s key executives is of great 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 importance to the organization’s success. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The writer would then assert that the contrary position has even greater 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 merit. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 . . . Yet chief executives of our most successful corporations would no 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 doubt admit that without the cooperative efforts of their subordinates, 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 their personal vision would never become reality. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—How to Put It All Together 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere again are the notes on Issue Statement 3. The test-taker has now 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbered his notes to indicate how he plans to organize his essay. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PRO CON 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 1 self-interest rules lawmakers pander 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 ind. & bus. but accountable 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 e.g. auto emissions to voters 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but nations too 2 12345678901234567890123456789012123456789012345678901 enforcement problems 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 14 environ problems too e.g. bus. relocate 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 widespread for 13 bureaucratic problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ind. & bus. 2 12345678901234567890123456789012123456789012345678901 e.g. delays 2 12345678901234567890123456789012123456789012345678901 but nations must 2 12345678901234567890123456789012123456789012345678901 e.g. compromises 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cooperate 2 12345678901234567890123456789012123456789012345678901 e.g. admin. expense 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must put up but 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 with problems to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 save environ. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N otice that the test-taker has decided to begin and end the body of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essay with “ pro” points, possibly because he weighed the evidence—the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pros and cons—and thinks the “ pro” points are the strongest arguments. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 H e probably intends to agree, at least on balance, with the statement. Also 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 109

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 notice that he plans to discuss two distinct “ cons” both in the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph (2), possibly because he doesn’t have enough to say about them 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to justify devoting an entire paragraph to either one alone. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 N ow here’s a full length essay on Issue Statement 3, which pulls together 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the techniques you have learned about up to this point in the lesson. It runs 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 about 430 words in length—a bit longer than average, but still realistic 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 given a 30-minute time limit. Certain words and phrases that you might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use in almost any Issue essay are underlined—just to help you see how the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ideas flow naturally and persuasively from one to the next. (The test’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 built-in word processor does not provide for underlining.) N otice the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 following features of the essay, which together boost the essay to the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 highest score level: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The essay expresses overall but qualified agreement with the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 statement, a thoughtful viewpoint that shows the writer recognizes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the issue’s complexity. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The body of the essay begins and ends with “ pro” arguments for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rhetorical impact. The “ con” arguments are positioned between 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 them. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • For each of the “ con” arguments (third and fourth paragraphs), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the writer immediately responds with persuasive counterpoints. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice also that the writer tried to follow his outline, while at the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time remaining flexible as new ideas for content or organization occurred 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to him. (N otice, for instance, that he repositioned certain points from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outline.) Also notice that the writer didn’t incorporate every single point 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from his outline, perhaps because he simply didn’t have time in 30 minutes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to cover every point. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Essay (Issue Statement 3) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In asserting that government regulation is the “ best” way to ensure 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 environmental protection, the speaker fails to acknowledge certain 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 problems inherent with government regulation. N evertheless, I 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 agree with the statement to the extent that exclusive reliance on 2 2 12345678901234567890123456789012123456789012345678901 individual or business volunteerism would be naive and impru- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dent, especially considering the stakes involved. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Experience tells us that individuals and private corporations tend 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to act in their own short-term economic and political interest, not 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on behalf of the environment or the public at large. For example, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 current technology makes possible the complete elimination of 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 polluting emissions from automobiles. N evertheless, neither auto- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 mobile manufacturers nor consumers are willing or able to 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 110 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 voluntarily make the short-term sacrifices necessary to accomplish 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this goal. O nly the government holds the regulatory and enforce- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment power to impose the necessary standards and to ensure that 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 we achieve these goals. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Admittedly, government penalties do not guarantee compliance 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 with environmental regulations. Businesses often attempt to avoid 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compliance by concealing their activities, lobbying legislators to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 modify regulations, or moving operations to jurisdictions that 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 allow their environmentally harmful activities. O thers calculate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the cost of polluting, in terms of punishment, then budget in 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 advance for anticipated penalties and openly violate the law. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H owever, this behavior only serves to underscore the need for 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 government intervention, because left unfettered this type of 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 behavior would only exacerbate environmental problems. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O ne must admit as well that government regulation, environmen12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 tal or otherwise, is fraught with bureaucratic and enforcement 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 problems. Regulatory systems inherently call for legislative com- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mittees, investigations, and enforcement agencies, all of which add 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to the tax burden on the citizens whom these regulations are 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 designed to protect. Also, delays typically associated with bureau- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 cratic regulation can thwart the purpose of the regulations, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because environmental problems can quickly become grave 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 indeed. H owever, given that unjustifiable reliance on volunteerism 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is the only alternative, government regulation seems necessary. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 M oreover, such delays seem trivial when we consider that many 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 environmental problems carry not only a real threat to public 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 health but also a potential threat to the very survival of the human 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Finally, environmental issues inherently involve public health and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 are far too pandemic in nature for individuals or even businesses to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 solve on their own. M any of the most egregious environmental 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 violations traverse state and sometimes national borders. Individu12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 als and businesses have neither the power nor the resources to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 address these widespread hazards. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In the final analysis, only the authority and scope of power that a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 government possesses can ensure the attainment of agreed-upon 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 environmental goals. Since individuals are unable and businesses 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 are by nature unwilling to assume this responsibility, government 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must do so. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 111

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue Analysis—Rhetorical Effectiveness and 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your Essay’s Structure 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow you arrange your ideas into paragraphs can make a big difference in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 your essay’s persuasiveness. Chapter 2 introduced the basic strategy of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 starting the body of your essay with your best argument and finishing it 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 with your second-best argument, sandwiching your other arguments 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between these two. And, you just saw in the preceding essay how you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adapt this strategy to a two-column list of “ pros” and “ cons” — 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 sandwiching the “ cons” in between the “ pros.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As an advanced test-taker, you should consider alternative structures as 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 well. Although the ways in which you can organize an Issue essay are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 limitless, five basic structures cover most situations. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the following templates, the term “ counterpoint” refers to a reason or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example supporting a contrary position, and “ rebuttal” refers to a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 response (reason or example) to a counterpoint (and in further support of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the other position). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Try this first structure if your agreement or disagreement with the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement is nearly unqualified. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1st Paragraph: M ain reason for your position → counterpoint → 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rebuttal 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2nd Paragraph: Second reason for your position → counterpoint → 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rebuttal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3rd Paragraph: Third reason for your position → counterpoint → 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rebuttal 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can use the same structure to discuss two or more examples (or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinct areas) that lend support to your position: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1st Paragraph: O ne example (or area) that supports your position → 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 counterpoint → rebuttal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2nd Paragraph: Another example (or area) that supports your position 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 → counterpoint → rebuttal 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3rd Paragraph: Another example (or area) that supports your position 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 → counterpoint → rebuttal 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Try this next structure to acknowledge one strong argument against your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 position, but where you have more reasons or examples in support of your 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 position. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 112 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1st Paragraph: O ne reason (and/or example) in support of your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2nd Paragraph: Another reason (and/or example) in support of your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3rd Paragraph: Another reason (and/or example) in support of your 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 position 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Final Paragraph: Chief counter-argument → rebuttal 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Try this next structure to acknowledge one or m ore strong arguments 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 against your position, but where you have better reasons and/or examples 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 in support of your position. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1st Paragraph: Chief counter-argument 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ex t Paragraph: Another counter-argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ex t Paragraph: O ne reason and/or example in support of your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ex t Paragraph: Another reason and/or example in support of your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If the arguments for and against the statement’s position are equally strong 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (e.g., if it all depends on the area under consideration), try the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 structure for a balanced essay: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1st Paragraph (or 1st and 2nd Paragraphs): Area(s) or examples 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supporting one position 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2nd Paragraph (or 3rd and 4th Paragraphs): Area(s) or examples 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supporting a contrary position 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Finally, try the following structure to address two or more reasons in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 support of an opposing position, each one in turn: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1st Paragraph (or 1st and 2nd Paragraphs): Counter-argument → 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rebuttal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2nd Paragraph (or 3rd and 4th Paragraphs): Counter-argument → 2 12345678901234567890123456789012123456789012345678901 rebuttal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext Paragraph: Counter-argument → rebuttal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 113

Part II: A nalytical W riting A ssessm ent

Alert!

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You need not adhere strictly to one of these structures in order to write an 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effective Issue essay. Try to be flexible. The particular ideas you’ve jotted 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 down might come together best in some other, idiosyncratic format. In 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 short, let your ideas drive your essay’s structure, not vice versa. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument Analysis—Common Reasoning 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Flaws and How to Handle Them 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this section, you’ll turn your attention from the Issue-Analysis writing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 task to the Argument-Analysis task. The test-maker intentionally incorpo- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 rates into each Argument numerous reasoning flaws that render the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument vulnerable to criticism. In a typical Argument, you can find 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 three or four distinct areas for critique. The following are the most 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 common types of problems with GM AT Arguments (memorize this list to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 help you brainstorm and ferret out flaws in any GM AT Argument): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Confusing cause-and-effect with mere correlation or time sequence 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Drawing a weak analogy between two things 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Relying on a potentially unrepresentative statistical sample 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Relying on a potentially unreliable survey or poll 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Assuming that a certain condition is necessary and/or sufficient for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a certain outcome 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Assuming that characteristics of a group apply to each group 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 member (or vice-versa) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Assuming that all things remain unchanged over time 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Assuming that two courses of action are mutually exclusive 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Relying on undefined, vague, or ambiguous terms 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the following pages, you’ll learn more about each type of flaw, and 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you’ll learn how to address each one in your Argument-Analysis essay. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The sample Arguments you’ll read in this section are each designed to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 focus on one particular reasoning flaw. Keep in mind: M ost Arguments in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the official pool are a bit longer and more involved. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 114 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Confusing Cause-and-Effect with Mere Correlation 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or Time Sequence 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any GM AT Arguments rely on the claim that certain events cause other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain events. A cause-and-effect claim might be based on: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1. A significant correlation between the occurrence of two phenom- 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ena (both phenomena generally occur together) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. A tem poral relationship between the two (one event occurred 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 after another) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A significant correlation or a temporal relationship between two 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 phenomena is one indication of a cause-and-effect relationship between 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them. H owever, neither in itself suffices to prove such a relationship. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Unless the Argument also considers and eliminates all other plausible 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 causes of the presumed “ result” (by the way, it won’t), the Argument is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 vulnerable to criticism. To show the reader you understand this sort of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 false-cause problem, you need to accomplish all three of the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tasks: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the false-cause problem (e.g., as one of the Argument’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 crucial assumptions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two examples of other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible causes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Ex plain how the false-cause problem undermines the Argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that confuses causation with mere tem poral sequence, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 followed by a succinct and effective critique. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The following appeared in the editorial section of a newspaper: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Two years ago State X enacted a law prohibiting environmental 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 emissions of certain nitrocarbon byproducts, on the basis that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 these byproducts have been shown to cause Urkin’s disease in 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 humans. Last year fewer State X residents reported symptoms of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Urkin’s disease than in any prior year. Since the law is clearly 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 effective in preventing the disease, in the interest of public health 2 12345678901234567890123456789012123456789012345678901 22 this state should adopt a similar law.” 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The editorial infers that State X’s new law is responsible for the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 apparent decline in the incidence of Urkin’s disease (UD) symp- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 toms. H owever, the editorial’s author ignores other possible causes 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of the decline—for example, a new UD cure or new treatment for 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 115

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 UD symptoms. Without eliminating alternative explanations such 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as these, the author cannot justify either the inference or the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional assertion that a similar law would be similarly effective 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 in the author’s state. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Drawing a Weak Analogy Between Two Things 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT Argument might draw a conclusion about one thing (perhaps a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 city, school, or company) on the basis of an observation about a similar 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thing. H owever, in doing so, the Argument assumes that because the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 things are similar in certain respects, they are similar in all respects, at least 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 as far as the Argument is concerned. Unless the Argument provides 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sufficient evidence to substantiate this assumption (by the way, it won’t), 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the Argument is vulnerable to criticism. The Argument cannot rely on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these claims to support its recommendation. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To show the reader you understand the weak-analogy problem, you need 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to accomplish all three of the following tasks: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Identify the analogy (e.g., as one of the Argument’s crucial 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two significant ways in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which the two things might differ. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Ex plain how those differences, which render the analogy weak, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 undermine the Argument’s conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that contains a questionable analogy, followed by an 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effective 3-sentence analysis. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following was part of a speech made by the principal of Valley 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H igh School: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Every year Dunston H igh School wins the school district’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 student M ath SuperBowl competition. The average salary of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 teachers at Dunston is greater than at any other school in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 district. H ence in order for Valley H igh students to improve their 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scores on the state’s standardized achievement exams, Valley 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 should begin awarding bonuses to Valley teachers whenever Valley 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 defeats Dunston in the M ath SuperBowl.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The principal’s recommendation relies on what might be a poor 2 2 12345678901234567890123456789012123456789012345678901 analogy between Dunston and Valley. Valley teachers might be less 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 responsive than Dunston teachers when it comes to monetary 2 1 2 116 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incentives, or Valley students might be less gifted than Dunston 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 students when it comes to math. In short, what might have helped 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dunston perform well at the M ath SuperBowl would not 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 necessarily help Valley perform better either at the SuperBowl or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the state exams. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Some GM AT Arguments actually rest on m ore than one weak analogy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Earlier in the chapter, you saw a simulated example—Argument 1 (page 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 85) relied on two distinct analogies. The second and fourth body 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraphs of the Argument’s response (page 91) addressed each one, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respectively. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Relying on a Potentially Unrepresentative 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Statistical Sample 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A GM AT Argument might cite statistical evidence from a study, survey, or 2 12345678901234567890123456789012123456789012345678901 poll involving a “ sample” group, then draw a conclusion about a larger 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group or population which the sample supposedly represents. But in order 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for a statistical sample to accurately reflect a larger population, the sample 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must meet two requirements: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The sample must be significant in size (number) as a portion of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the overall population. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The sample must be representative of the overall population in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms of relevant characteristics. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Arguments that cite statistics from studies, surveys, and polls often fail to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 establish either of these two requirements. O f course this failure is by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 design of the test-maker, who is inviting you to call into question the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reliability of the evidence. To show the reader you understand this 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 statistical problem, you need to accomplish all three of the following tasks: 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the problem (e.g., as one of the Argument’s crucial 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two respects in which key 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 characteristics of a sample group might differ from those of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 larger population. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Ex plain how those differences would undermine the Argument’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that relies on tw o potentially unrepresentative sample 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 groups: (1) new graduates from a certain state’s undergraduate programs 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and (2) new graduates from the state’s graduate-level programs. The 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 response that follows it provides a brief but effective critique. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 117

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Chapter 3: Analytical Writing Assessment

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following was part of an article appearing in a national magazine: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ O ur nation’s new college graduates will have better success 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 obtaining jobs if they do not pursue advanced degrees after 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 graduation. After all, more than ninety percent of State X’s 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 undergraduate students are employed full-time within one year 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 after they graduate, while less than half of State X’s graduate-level 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 students find employment within one year after receiving their 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 graduate degrees.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Response: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The argument fails to consider that State X’s new graduates might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not be representative of the nation’s as a whole, especially if the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 former group constitutes only a small percentage of the latter 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group. If it turns out, for example, that State X’s undergraduate 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 students are less motivated than the nation’s average college 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 student to pursue graduate-level study, then the argument’s 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recommendation for all undergraduate students would be unwar- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ranted. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Relying on Tainted Results from a Survey or Poll 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you just learned, a GM AT Argument might draw some conclusion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving a group based on statistical data about an insufficient or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unrepresentative sample. H owever, this is not the only potential problem 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with statistical data. The process of collecting the data (i.e., the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 methodology) might be flawed in a way that calls into question the quality 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the data, rendering the data “ tainted” and therefore unreliable for the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 purpose of drawing any conclusions. In order for survey or poll results to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be reliable in quality: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The survey or poll responses must be credible (truthful and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accurate). If respondents have reason to provide incomplete or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 false responses, the results are tainted (and therefore unreliable). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The method of collecting the data must be unbiased. If responses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are not mandatory, or if the survey’s form predisposes subjects to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 respond in certain ways, then the results are tainted (and therefore 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unreliable). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • To show the reader that you recognize and understand this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statistical problem, you need to accomplish all three of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 following tasks: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 118 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. Identify the problem (e.g., as one of the Argument’s crucial 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two reasons, based on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Argument’s information, why the statistical data might be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tainted (and therefore unreliable). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3. Ex plain how the potentially tainted data might undermine 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Argument’s conclusion. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 The following Argument relies on a survey that poses a potential bias as 2 2 12345678901234567890123456789012123456789012345678901 well as a credibility problem. The response contains all three elements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 required to address each problem, in a single paragraph. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The following appeared in a memo from the director of human 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 resources at Webco: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Among Webco employees participating in our department’s most 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 recent survey, about half indicated that they are happy with our 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 current four-day work week. These survey results show that the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 most effective way to improve overall productivity at Webco is to 2 2 12345678901234567890123456789012123456789012345678901 allow each employee to choose for himself or herself either a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four-day or five-day work week.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The survey methodology might be problematic in two respects. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 First, we are not informed whether the survey required that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respondents choose their work week preference between alterna12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 tives. If it did, then the results might distort the preferences of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 respondents, who might very well prefer a work schedule choice 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 not provided for in the survey. Secondly, we are not informed 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 whether survey responses were anonymous, or even confidential. If 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 they were not, then respondents might have provided responses 2 12345678901234567890123456789012123456789012345678901 that they believed their superiors would approve of, regardless of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whether the responses were truthful. In either event, the survey 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 results would be unreliable for the purpose of drawing any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusions about Webco employee preferences, let alone about 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 how to improve overall productivity at Webco. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 119

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Assuming That a Certain Condition is Necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and/or Sufficient for a Certain Outcome 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT Argument might recommend a certain course of action, based on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one or both of the following claims: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. The course of action is necessary to achieve a desired result. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. The course of action is sufficient to achieve the desired result. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 With respect to claim 1, the Argument must provide evidence that no other 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 means of achieving the same result are available (by the way, it won’t). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 With respect to claim 2, the Argument must provide strong evidence that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 the proposed course of action by itself would be sufficient to bring about 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the desired result (by the way, it won’t). Lacking this sort of evidence, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument cannot rely on these claims to support its recommendation. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To show the reader you understand necessary-condition and sufficient- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 condition problems, you need to accomplish all three of the following 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 tasks: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Identify the problem (e.g., as one of the Argument’s crucial 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 assumptions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two examples. For a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 necessary-condition problem, suggest other possible means of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 achieving the stated objective. For a sufficient-condition problem, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggest other conditions that might also be necessary for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outcome. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Ex plain how the problem undermines the Argument’s conclusion. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that assumes that a certain condition is necessary for 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 a certain outcome. The response provides a brief but incisive analysis of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following appeared in a memo from a vice president at Toyco, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which operates a large chain of toy stores: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Last year was the first year in which Playtime Stores, our main 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 competitor, sold more toys than Toyco. Playtime’s compensation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for its retail sales force is based entirely on their sales. If Toyco is to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recapture its leadership position in the toy-sales market, we must 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reestablish our former policy of requiring all our retail associates 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to meet strict sales quotas in order to retain their jobs.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 120 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The argument assumes that the proposed compensation policy is 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the only way that Toyco can once again sell more toys than 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Playtime. H owever, the vice president fails to consider and rule out 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible alternative means of achieving this end—for example, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 opening new stores or adding new types of toys to the ones its 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stores already carry. Until the president does so, I will remain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unconvinced that the proposed policy is a necessary means for 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Toyco to recapture market leadership. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Earlier in the chapter, Argument 1 (about UpperCuts hair salon) relied on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a sufficient-condition assumption. Read again the third body paragraph 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of the response to that Argument (page 91), which addresses the problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Assuming That Characteristics of a Group Apply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to Each Group Member (or vice-versa) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A GM AT Argument might point out some fact about a general 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 group—such as students, employees, or cities—to support a claim about 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 one particular member of that group. O r conversely, the Argument might 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 point out some fact about a particular group member to support a claim 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 about the entire group. In either scenario, unless the Argument supplies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear evidence that the member is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 representative of the group as a whole (by the way, it won’t), the Argument 2 12345678901234567890123456789012123456789012345678901 2 is vulnerable to criticism. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To show the reader you understand a group-member problem, you need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accomplish all three of the following tasks: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the problem (e.g., as one of the Argument’s crucial 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing at least one or two significant ways in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which the member might differ from the general group. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Ex plain how those key differences, which serve to refute the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumption, would undermine the Argument’s conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that assumes that characteristics of a group member 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 apply to the group as a whole. Following the Argument is a response that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shows how to handle the problem in one very succinct paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 121

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Chapter 3: Analytical Writing Assessment

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following is part of an article appearing in the entertainment 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 section of a local newspaper: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ At the local Viewer Choice video store, the number of available 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 movies in VH S-tape format remains about the same as three years 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ago, even though the number of available movies on digital video 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 disk, or DVD, has increased tenfold over the past three years. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 People who predict the impending obsolescence of the VH S format 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 are mistaken, since demand for VH S movie rentals today clearly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remains just as strong as ever.” 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This argument assumes that Viewer Choice (VC) is typical of all 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 video stores as a group. H owever, this isn’t necessarily the case; VC 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might carry far more VH S tapes, as a percentage of its total 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inventory, than the average store. If so, then the argument has 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 failed to discredit the prediction for the industry as a whole. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Assuming That All Things Remain Unchanged 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Over Time 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT Argument might rely on evidence collected in the past in order to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 formulate some conclusion or recommendation concerning the present or 2 12345678901234567890123456789012123456789012345678901 2 the future. Similarly, an Argument might rely on evidence about present 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conditions to make a prediction or recommendation for the future. But 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unless the Argument provides clear evidence that key circumstances have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remained, or will remain, unchanged over the relevant time period (by the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way, it won’t), the Argument is vulnerable to criticism. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To address this problem, you should accomplish each of the following 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three tasks: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Identify the problem (i.e., the poor assumption that all key 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circumstances remain fixed over time). 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Elucidate by providing examples of conditions that might change 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from one time frame to the other. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Evaluate the argument in light of the problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s an Argument that provides evidence about the past to draw a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 conclusion about the present as well as the future, followed by a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3-sentence paragraph that addresses the problem. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 122 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following appeared in a political campaign advertisement: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Residents of this state should vote to elect Kravitz as state 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 governor in the upcoming election. During Kravitz’s final term as a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 state senator, she was a member of special legislative committee 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 that explored ways the state can reduce its escalating rate of violent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 crime. Elect Kravitz for governor, and our cities’ streets will be 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 safer than ever.” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Response: 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Assuming that at one time Kravitz was genuinely committed to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 fighting violent crime, the ad unfairly infers a similar commitment 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on Kravitz’s part today and in the future while Kravitz serves as 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 governor. Kravitz might hold entirely different views today, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 especially if her participation as a member of the committee 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 occurred some time ago. Lacking better evidence that as governor 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Kravitz would continue to make crime fighting a high priority, the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ad cannot persuade me to vote for Kravitz based on her committee 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 membership. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Assuming That Two Courses of Action are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Mutually Exclusive 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 An Argument might recommend one course of action over another in 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 order to achieve the stated objective, without considering that it is possible 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to pursue both courses (that is, they are not mutually exclusive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternatives), thereby increasing the likelihood of achieving the objective. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a good example, along with a response that handles the flaw. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Rivertown’s historic H ill district used to be one of the city’s main 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 tourist attractions. Recently, however, the district’s quaint older 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 shops and restaurants have had difficulty attracting patrons. In 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 order to reverse the decline in tourism to the district, Rivertown’s 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 City Council intends to approve construction a new shopping 2 12345678901234567890123456789012123456789012345678901 22 center called H ill H ub on one of the district’s few remaining vacant 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parcels. H owever, the city’s interests in attracting revenue from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tourism would be better served were it to focus instead on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 restoring H ill district’s older buildings and waging a publicity 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 campaign touting the historically authentic character of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 district. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 123

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The argument seems to assume that the city must either approve 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the H ill H ub project or engage in the restoration and publicity 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 efforts that the argument suggests, but that the city cannot do 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both. H owever, the argument provides absolutely no evidence that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 the city must choose between the two courses of action. Lacking 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any such evidence, it is entirely possible that implementing both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plans would attract more dollars from tourists to the district than 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 implementing either one alone. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Relying on Undefined, Vague, or Ambiguous Terms 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An Argument might contain a statement (or word or phrase) that carries 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more than one possible meaning or is simply too vague to reasonably rely 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 upon when it comes to drawing conclusions. Look for references to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ some,” “ many,” and “ several” in lieu of providing precise percentages or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbers. Also look for references to a particular class, category, or group, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without a clear explanation of what it includes or excludes. H ere’s an 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 example, followed by an effective response: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A reliable recent study attests to the value of physical activity in 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 increasing attention span among young children. Accordingly, in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 order to improve the overall learning levels among elementary- 2 2 12345678901234567890123456789012123456789012345678901 school children in our state, the state’s board of education should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mandate a daily exercise regimen for students at all our state’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 elementary schools. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Response: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Argument neglects to indicate what types of “ physical 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 activity” the study observed. For all I know, those activities 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 amounted to play, as opposed to the recommended exercise 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ regimen,” which might be more like work for children. N or does 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Argument indicate the age range of the “ young children” 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 observed in the study. Perhaps the children were pre-schoolers, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whose attention spans might respond differently than school-age 2 2 12345678901234567890123456789012123456789012345678901 children to certain types of physical activity. In short, before I can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine the extent to which the study supports the recommenda- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion, I need specific definitions of these important terms. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 124 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 3: Analytical Writing Assessment

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument-Analysis—Adding Optional 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Elements to Your Essay 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The directive for every GM AT Argument indicates that you m ay include 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 either or both of the following in your essay: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Suggestions as to how the Argument can be strengthened 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Additional information needed to evaluate the Argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 These two elements are optional, and you can score high on your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Argument essay without them. Thus, do not take the time to add either of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 these two elements to your essay unless you’re sure you’ve adequately 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 addressed all of the Argument’s major problems. O therwise, you risk 2 2 12345678901234567890123456789012123456789012345678901 running out of time to accomplish that essential task. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But keep in mind: You’re more likely to attain a top score of 6 if you add 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 these additional elements, all else being equal. So, as you brainstorm your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument essay, by all means, jot down your ideas about how the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument can be strengthened and/or what additional information is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 needed to evaluate the Argument. Then, after you’ve finished your critique 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the Argument and proofread your critique, check the clock. If you still 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have at least a few minutes, go ahead and add one or both elements. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You have two realistic choices as to where to include them in your essay: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. List the suggestions (and/or additional information needed) in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your final, concluding paragraph. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Incorporate the suggestions (and/or additional information needed) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 into your body paragraphs. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s how you might incorporate both elements into a final paragraph of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an essay on Argument 1 about UpperCuts hair salon (we’ve underlined 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 words and phrases that you could use in the final paragraph of nearly any 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument essay): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Optional elements added to an essay’s final, concluding paragraph: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In sum, the argument is a dubious one that relies on a series of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unproven assumptions—about Apton’s and Brainard’s demographics, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the reasons for the success of the two other salons, and UC’s future 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 expenses. To strengthen the argument, the manager should provide 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 better evidence of a demographic shift in Apton toward the downtown 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 area, and clear evidence that those demographics portend success there 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 for an upscale hair salon. Even with this additional evidence, in order 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to properly evaluate the argument I would need to know why 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H air-Dooz relocated, what factors have contributed to the Brainard 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 salon’s success, what factors other than location might have contrib2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 125

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 uted to UC’s sagging profits at the mall, and what additional, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 offsetting expenses UC might incur at the new location. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow here’s how you might incorporate the same two elements into the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 body of an essay on the same Argument. (The optional elements are in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 italics—just to help you locate them.) Again, we’ve underlined words and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 phrases that you could use in nearly any Argument essay: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Optional elements incorporated into an essay’s body paragraphs: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 To begin with, the argument assumes that Apton’s demographic trend 2 2 12345678901234567890123456789012123456789012345678901 reflects the national trend. Yet, the mere fact that one hair salon has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 moved downtown hardly suffices to infer any such trend in Apton; 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H air-Dooz might owe its success at its new location to factors 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unrelated to Apton’s demographics. In fact, for all we know, the trend 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in Apton might be in the opposite direction. T hus, I w ould need to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 k now w hether m ore people are in fact m oving to dow ntow n A pton 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 before I could either accept or reject the m anager’s proposal. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Even if Apton’s demographics do reflect the national trend, it is unfair 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to assume that UC will attract more customers simply by relocating 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 downtown. It is entirely possible that the types of people who prefer 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 living in downtown areas tend not to patronize upscale salons. It is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 also possible that H air-Dooz will continue to impede upon UC’s 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 business, just as it might have at the mall. Before I can accept that UC 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w ould attract m ore custom ers dow ntow n, the m anager w ould need to 2 2 12345678901234567890123456789012123456789012345678901 supply clear proof of a sufficient dem and dow ntow n for UC’s service. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N or can the manager justify the recommended course of action on the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 basis of the Brainard salon’s success. Perhaps hair salons generally fare 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better in downtown Brainard than downtown Apton, due to demo12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 graphic differences between the two areas. O r perhaps the salon 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thrives only because it is long-established in downtown Brainard—an 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 advantage that UC clearly would not have in its new location. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A ccordingly, in order to determ ine w hether the success of the Brainard 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 salon portends success for UC in dow ntow n A pton, I w ould need to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 k now w hy the Brainard salon is successful in the first place. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Finally, even assuming that the proposed relocation would attract 2 2 12345678901234567890123456789012123456789012345678901 more customers, an increase in the number of patrons would not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily result in improved profits. After all, profit is a function of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expenses as well as revenue. Thus an increase in UC’s expenses—due 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perhaps to higher rents downtown than at the mall—might very well 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 offset increasing revenues, thereby frustrating UC’s efforts to improve 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 its profitability. Before I could agree w ith the proposal, I w ould need 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to ex am ine a com parative cost-benefit analysis for the tw o locations. 2 12345678901234567890123456789012123456789012345678901 2 1 2 126 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 3: Analytical Writing Assessment

Take It to the Next Level

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Writing Style and Mechanics 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you know by now, although GM AT readers place less weight on 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 writing style and mechanics than on content and organization, the way 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you write can affect your Analytical Writing Assessment score, especially if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ve written an otherwise borderline essay that has the reader “ on the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 fence” between two scores. (It happens frequently!) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Earlier in the chapter, you learned some basic tips for style and mechanics. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The N ext Level moves on to more advanced techniques. H ere, you’ll learn 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A variety of rhetorical devices that, if used appropriately and 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 prudently, add persuasiveness to essays (especially your Issue essay) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • H ow to connect your ideas together with words and phrases that 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 will help the reader follow your reasoning as you proceed from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one point to the next 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The parlance of Critical Reasoning, and how to use it properly (in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your Argument essay) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • H ow to refer to yourself, to the statement or Argument, and to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author of the statement or Argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As we’ve mentioned before, however, refinement and maturity in writing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 style come mainly with practice. So you should also apply what you learn 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here to the practice tests in Part V of this book. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Developing a Persuasive Writing Style 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Earlier in this lesson, you learned how to develop persuasive ideas (espe- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cially for your Issue essay) and to structure and sequence your paragraphs 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in ways that enhance their persuasiveness. To further ensure a high Ana- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 lytical Writing Assessment score, you should try to use particular words 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and phrases that can be especially effective rhetorically, but you should 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 avoid words and phrases that amount to so-called “ empty rhetoric.” You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can also use irony, and even punctuation, for rhetorical emphasis. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Rhetorical words and phrases—by functional category 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a reference list of rhetorical words and phrases, categorized by 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 function. Some list items you encountered as underlined words and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 phrases in the examples throughout previous chapters, while others 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are new. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 127

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to subordinate an idea: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 although it might appear that, at first glance it would seem/appear 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that, admittedly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to argue for a position, thesis, or viewpoint: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 promotes, facilitates, provides a strong impetus, serves to, directly, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 furthers, accomplishes, achieves, demonstrates, suggests, indicates 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to argue for a solution or direction based on 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 public policy or some other normative basis: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ultimate goal/objective/purpose, overriding, primary concern, subordi2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 nate, subsumed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to refute, rebut, or counter a proposition, theory, 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 or viewpoint: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 however, closer scrutiny reveals, upon closer inspection/examination, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 a more thorough analysis, in reality, actually, when viewed more 2 2 12345678901234567890123456789012123456789012345678901 closely, when viewed from another perspective, further observation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shows 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to point out problems with a proposition, theory, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or viewpoint: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 however, nevertheless, yet, still, despite, of course, serious drawbacks, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problematic, countervailing factors 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to argue against a position or viewpoint: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 works against, undermines, thwarts, defeats, runs contrary to, fails to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 achieve/promote/accomplish, is inconsistent with, impedes 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use phrases such as these to argue that the merits of one position outweigh 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 those of another 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 on balance, on the whole, all things considered, in the final analysis 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To improve your power of persuasion, again, there’s no substitute for 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 practice. So you should try to incorporate these words and phrases into 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 your essays as you take the practice tests in Part V of this book. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 128 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 3: Analytical Writing Assessment

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Avoid empty rhetoric 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any test-takers try to mask weak ideas by relying on strong rhetoric. Be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 careful in using words and phrases such as these for emphasis: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 clearly, absolutely, definitely, without a doubt, nobody could dispute 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that, extremely, positively, emphatically, unquestionably, certainly, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 undeniably, without reservation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It’s okay to use these phrases. But keep in mind: By themselves, they add 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 absolutely no substance to your ideas. So be sure that you have convincing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasons and/or examples to back up your rhetoric! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Using irony as a rhetorical device 2 12345678901234567890123456789012123456789012345678901 In your Issue essay, look for the opportunity to use words in their ironic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense or as misnomers for rhetorical emphasis—in other words, to help 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 make your point. Read the Issue statement closely for key words. H ere’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one example of each: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Example (irony): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The speaker fails to consider the long-term cultural impact of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 kinds of technological “ advancements” I’ve just described. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Example (misnomer): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The “ knowledge” to which the statement refers is, in actuality, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only subjective perception. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Be sure to use quotation marks for the ironic term or misnomer, whether 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or not you’re quoting the Issue statement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Using punctuation for rhetorical emphasis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can also use punctuation for rhetorical emphasis. H ere are some 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 suggestions (try them out during the practice tests in Part III): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Use em-dashes (two hyphens, or one hyphen preceded and followed 2 12345678901234567890123456789012123456789012345678901 by a space) in the middle of a sentence—instead of commas or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parentheses—to set off particularly important parenthetical mate- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rial (just like in this sentence). You can also use an em-dash before a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concluding phrase instead of a comma—to help set off and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 emphasize what follows (just like in this sentence). But don’t overuse 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the dash—or it will lose its punch (as in this paragraph). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Use exclamation points for emphasis very sparingly. As in this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph, one per essay is plenty! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Sentences that pose questions can be a useful rhetorical device. Like 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 short, abrupt sentences, rhetorical questions can help persuade the 2 2 12345678901234567890123456789012123456789012345678901 1 reader—or at least help to make your point. They can be quite 2 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 129

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 effective, especially in Issue essays. They also add interest and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 variety. Yet how many test-takers think to incorporate them into 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their essays? N ot many. (By the way, we just posed a rhetorical 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 question.) Just be sure to provide an answer to your question. And 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t overdo it; one rhetorical question per essay is plenty. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 • Avoid using UPPERCASE letters, *asterisks* or similar devices to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 flag words you would emphasize in rhetorical speech. To get your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point across, rely instead on your choice of words and phrases as 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 well as your sentence construction. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 As noted in Part I, the testing system’s word processor does not permit the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use of attributes such as bold, underlining, and italics—so those devices 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are not available for emphasis in any event. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Connecting Your Ideas Together 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your essays will not earn top scores unless your ideas flow naturally from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one to the next, allowing the reader to easily follow your train of thought. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To connect your ideas, develop your own arsenal of transition devices— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 words and phrases that serve as bridges between ideas—helping to convey 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 your line of reasoning to the reader. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each transition device should help the reader make certain connections or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 assumptions about the two areas that you are connecting. For example, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some devices lead your reader forward and imply the building of an idea or 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thought, while others prompt the reader to compare ideas or draw 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusions from the preceding thoughts. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a reference list that includes many of those devices—by functional 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 category. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To signal addition: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and, again, and then, besides, equally important, finally, further, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 furthermore, nor, too, next, lastly, what’s more 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To connect ideas together: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 furthermore, additionally, in addition, also, [first, second, . . .], 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 moreover, most important/significantly, consequently, simultaneously, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concurrently, next, finally 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To signal comparison or contrast: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 but, although, conversely, in contrast, on the other hand, whereas, but, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 except, by comparison, where, compared to, weighed against, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 vis-à-vis, while, meanwhile 2 1 2 130 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To signal proof: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because, for, since, for the same reason, obviously, evidently, further12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more, moreover, besides, indeed, in fact, in addition, in any case, that is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To signal exception: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 yet, still, however, nevertheless, in spite of, despite, of course, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occasionally, sometimes, in rare instances, infrequently 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To signal sequence (chronological, logical, or rhetorical): 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 [first, second(ly), third(ly), . . .], next, then, now, at this point, then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 after, in turn, subsequently, finally, consequently, previously, before2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 hand, simultaneously, concurrently 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To signal examples: 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for example, for instance, perhaps, consider, take the case of, to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 demonstrate, to illustrate, as an illustration, one possible scenario, in 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 this case, in another case, on this occasion, in this situation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To signal your reasoning from premise to conclusion: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 therefore, thus, hence, accordingly, as a result, it follows that, hence, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 therefore, accordingly, thus, as a result, in turn 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Use these phrases for your concluding or summary paragraph: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in sum, in the final analysis, in brief, summing up, in conclusion, to 2 12345678901234567890123456789012123456789012345678901 2 conclude, to recapitulate, in essence, in a nutshell 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For insights and ideas about how use these transition words and phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in your GM AT essays, read again the sample essays earlier in this chapter. 2 12345678901234567890123456789012123456789012345678901 Look particularly at the underlined words and phrases; they provide the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 glue to connect together the pieces of those essays. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Using the Language of Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In your essays, you don’t need to resort to the technical terminology of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 formal logic. H owever, you will need to use less technical words, such as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ argument,” “ assumption,” “ conclusion,” and possibly “ premise” and 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ inference” —especially in your Argument essay. Be sure you understand 2 12345678901234567890123456789012123456789012345678901 what these words mean and that your use of them is idiomatic. H ere are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 definitions for these terms and usage guidelines. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument: The process of reasoning from premises to conclusion 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To describe a flawed argument, use adjectives such as w eak , poor, un- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sound, poorly reasoned, dubious, poorly supported, and problem atic. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 131

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Chapter 3: Analytical Writing Assessment

Part II: A nalytical W riting A ssessm ent

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To describe a good argument use adjectives such as strong, convincing, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w ell reasoned, and w ell supported. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You don’t “ prove an argument” ; rather, you “ prove an argument (to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be) true.” (H owever, the word “ prove” implies deduction and should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be used sparingly, if at all, in your Argument essay.) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Premise: A proposition helping to support an argument’s conclusion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Use the words prem ise and evidence interchangeably to refer to stated 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 information that is not in dispute. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Assumption: Something taken for granted to be true in the argument. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 (Strictly speaking, assumptions are unstated, assumed premises.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To describe an assumption, use adjectives such as unsupported, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unsubstantiated, and unproven. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To describe a particularly bad assumption, use adjectives such as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unlik ely, poor, questionable, doubtful, dubious, and im probable. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To strengthen an argument, you substantiate an assumption or prove 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (or show or dem onstrate) that the assumption is true. (H owever, be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 careful in using the word prove; it is a strong word that implies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deduction.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Strictly speaking, an assumption is neither “ true” nor “ false,” neither 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ correct” nor “ incorrect.” Also, you don’t “ prove an assumption.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: A proposition derived by deduction or inference from the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 premises of an argument. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To describe a poor conclusion, use adjectives such as indefensible, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unjustified, unsupported, im probable, and w eak . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To describe a good conclusion, use adjectives such as w ell-supported, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 proper, probable, w ell-justified, and strong. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although you can “ prove a conclusion” or “ provide proof for a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion,” again the word “ proof” implies deduction. You’re better 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 off “ supporting a conclusion” or “ showing that the conclusion is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probable.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Inference: The process of deriving from assumed premises (assumptions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 either a strict conclusion or a conclusion that is to some degree probable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can describe an inference as poor, unjustified, im probable, or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unlik ely. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can also describe an inference as strong, justified, probable, or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lik ely. 2 12345678901234567890123456789012123456789012345678901 2 1 2 132 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 You can “ infer that . . .” , but the phrase “ infer a conclusion” is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awkward. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Deduction: The process of reasoning in which the conclusion follows 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily from the premises. (Deduction is a specific kind of inference.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Arguments do not involve deduction; all inferences and conclu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sions involve probabilities, not certainties. So there’s no reason to use any 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 form of the word “ deduction” in your Argument essay. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 References to Yourself and to the Statement or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In your essay, occasionally you’ll need to refer to the Issue statement (or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Argument) as well to its hypothetical source, whether a person or entity. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 You might also wish to refer to yourself from time to time. H ere are some 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 guidelines for handling these references. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Self-references 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Self-references—singular as well as plural—are perfectly acceptable, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 though optional. Just be consistent. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ I disagree with . . .” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ In my view, . . .” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Without additional evidence, we cannot assume that . . .” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 References to the statement or Argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In your Issue essay, refer to the statement as “ this statement” or an 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative such as “ this claim” or “ this assertion.” In your Argument 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 essay, try using “ argument” to refer to the passage’s line of reasoning as a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whole, or “ recommendation” or “ claim” to refer to specific conclusions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 References to the source of the statement or Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Be sure your references to a statement or Argument’s source are 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 appropriate. In your Issue essay, you can simply refer to the statement’s 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 source as the “ speaker,” for example. In your Argument essay, the first 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time you refer to the source, be specific and correct—e.g., “ this editorial,” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ the ad,” “ the vice president,” or “ ACM E Shoes.” If no specific source is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provided, try using “ author” or “ argument.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 133

Take It to the Next Level

Alert!

Chapter 3: Analytical Writing Assessment

Part II: A nalytical W riting A ssessm ent

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Pronoun references to an Argument’s proponent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In your Argument essay, it’s okay to save keystrokes by using an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occasional pronoun. Just be sure that your pronouns are appropriate and 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 consistent (male, female, or neither): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The speaker argues . . . H er line of reasoning is . . . but she overlooks. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 . . .” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The manager cites . . . in support of his argument . . . H e then 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 recommends . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ To strengthen its conclusion, the city council must . . . It must also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 . . .” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, be sure that your pronoun references are clear. If a pronoun is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 separated from its antecedent (the noun that it describes) by one or more 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sentences, don’t use a pronoun. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Readers will disregard whether you use masculine, feminine, or gender- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 neutral terms in your essays. In other words, don’t worry about your 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 political correctness (or incorrectness) when it comes to gender. If you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wish to use gender-neutral pronouns, that’s fine. H owever, avoid 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternating male and female examples and expressions; you might confuse 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the reader. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Shorthand references to an Argument’s source and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evidence 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It’s perfectly acceptable to save keystrokes with shorthand names or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 acronyms in place of multiple-word proper nouns. If you use an acronym, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be sure to identify it the first time you use it. For example: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In this Argument, the marketing director for Specialty M anufacturing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (SM ) recommends that SM discontinue its line of. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Quoting the statement or Argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 O ccasionally, it may be appropriate to quote key words or phrases from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Issue statement or Argument. For example, you may wish to point out to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the reader a key phrase that is ambiguous or vague (e.g., “ certain respon- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dents” ), or a term that is overly inclusive or exclusive (e.g., “ only” or “ all” ). 2 2 12345678901234567890123456789012123456789012345678901 Just keep the number of quoted words and phrases to a minimum. Also, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 there’s never any justification for quoting entire sentences. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 134 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

PART

III Quantitative Ability Problem Solving

136

Data Sufficiency

164

M ath Review—N umber Forms, Relationships, and Sets

190

M ath Review—N umber Theory and Algebra M ath Review—Geometry

230

279

PART III

Chapter

4 Problem Solving 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to GM AT Problem Solving. In this chapter, you’ll: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn a step-by-step approach to handling any Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn success keys for tackling Problem Solving questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To handle GM AT Problem Solving questions, you’ll need to be well versed 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in the fundamental rules of arithmetic, algebra, and geometry. Your 2 2 12345678901234567890123456789012123456789012345678901 knowledge of these basics is, to a large extent, what’s being tested. (That’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what the math reviews in Chapters 5–7 are all about.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But, the test-makers are just as interested, if not more interested, in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 gauging your mental agility, flexibility, creativity, and efficiency when it 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 comes to solving quantitative problems. M ore specifically, they design 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving questions to help determine the following: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Can you manipulate numbers with a certain end result already in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mind? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Can you see the dynamic relationships between numbers as you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 apply operations to them? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Can you visualize geometric shapes and relationships between 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shapes? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Can you devise unconventional solutions to conventional quantita- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tive problems? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Can you solve problems efficiently, by recognizing the easiest, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quickest, or most reliable route to a solution? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 This chapter will help give you the skills you need to answer “ yes” to these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions. What follows might strike you as merely a series of tips, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 shortcuts, or secrets for GM AT Problem Solving. H owever, the skills you’ll 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 learn here are intrinsic to the test—and along with your knowledge of 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 136

Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 substantive rules of math—they’re precisely what Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions are designed to measure. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving—Your 5-Step Game Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The first task in this chapter is to learn the five basic steps for handling any 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 GM AT Problem Solving question. You’ll apply these steps to three sample 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sample Questions 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Q uestion 1 is a word problem involving changes in percent. (Word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems account for about half of the Q uantitative questions.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. If Susan drinks 10% of the juice from a 16-ounce bottle immedi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ately before lunch and 20% of the remaining amount with lunch, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 approximately how many ounces of juice are left to drink after 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lunch? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4.8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5.5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 11.2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 11.5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 13.0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 This next Problem Solving question involves the concept of arithm etic 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m ean (simple average). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The average of 6 numbers is 19. When one of those numbers is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 removed, the average of the remaining 5 numbers is 21. What 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 number was taken away? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 9 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 11 2 12345678901234567890123456789012123456789012345678901 E. 20 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 137

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a somewhat more difficult Problem Solving question. This one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involves the concept of proportion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. If p pencils cost 2q dollars, how many pencils can you buy for c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cents? [N ote: 1 dollar 5 100 cents] 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 pc 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2q 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 pc 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 200q 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 50pc 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 q 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2pc 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 c 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 200pcq 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N otice that instead of performing a numerical computation, your task in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question 3 is to ex press a com putational process in terms of letters. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Expressions such as these are known as literal ex pressions, and they can 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 be perplexing! O n the GM AT, you’ll probably find two or three of them 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among the 25–26 Problem Solving questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The 5-Step Plan 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the 5-step approach that will help you to handle any Problem 2 2 12345678901234567890123456789012123456789012345678901 Solving question. Just a few pages ahead, we’ll apply this approach our 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three sample Problem Solving questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: Size up the question. Read the question and then pause for a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 moment to ask yourself: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What specific subject area is being covered? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What rules and formulas are likely to come into play? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • H ow complex is this question? (H ow many steps are involved in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 solving it? Does it require setting up equations, or does it require 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 merely a few quick calculations?) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Do I have a clue, off the top of my head, how I would begin 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solving this problem? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Determine how much time you’re willing to spend on the problem, if any. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Recognizing a “ toughie” when you see it may save you valuable time; if 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you don’t have a clue, take a guess and move on. 2 12345678901234567890123456789012123456789012345678901 2 1 2 138 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

N ote

Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Remember: The computerized GM AT testing system determines the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficulty level of your questions based on your responses to prior 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 questions. So if you respond incorrectly to toughies, you’ll see fewer of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them later in your Q uantitative section. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Step 2: Size up the answer choices. Before you attempt to solve the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem at hand, examine the answer choices. They can provide helpful clues 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 about how to proceed in solving the problem and about what sort of solution 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you should be aiming for. Pay particular attention to the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 • Form : Are the answer choices expressed as percentages, fractions, or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 decimals? O unces or pounds? M inutes or hours? If the answer 2 2 12345678901234567890123456789012123456789012345678901 choices are expressed as equations, are all variables together on one 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 side of the equation? As you work through the problem, rewrite 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers and expressions to the same form as the answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Value: Are the answer choices extremely small valued numbers? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N umbers between 1 and 10? Greater numbers? N egative or positive 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers? Do the answer choices vary widely in value, or their 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 values clustered closely around an average? If all answer choices are 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 tightly clustered in value, you can probably disregard decimal points 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and extraneous zeros in performing calculations. At the same time, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 however, you should be more careful about rounding off your 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 figures where answer choices do not vary widely. Wide variation in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 value suggests that you can easily eliminate answer choices that 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 don’t correspond to the general value of number suggested by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the question. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • O ther distinctive properties and characteristics: Are the answer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices integers? Do they all include a variable? Do one or more 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 include radicals (roots)? Exponents? Is there a particular term, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 expression, or number that they have in common? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 3: Look for a shortcut to the answer. Before plunging headlong 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 into a problem, ask yourself if there’s a quick, intuitive way to get to the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 correct answer. If the solution is a numerical value, perhaps only one 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choice is in the right ballpark. Also, some questions can be solved 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 intuitively, without resort to equations and calculations. (You’ll see how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 when we apply this step to our sample questions.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 4: Set up the problem and solve it. If your intuition fails you, grab 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your pencil, roll up your sleeves, and do whatever computations, algebra, or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other procedures are needed to solve the problem at hand. Simple problems 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 may require just a few quick calculations, while complex algebra and geom12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 etry questions may require setting up and solving a series of equations. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 139

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 5: Verify your response before moving on. After solving the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem, if your solution does not appear among the answer choices, go 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 back and check your work. (You obviously made at least one mistake.) If 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 your solution does appear among the choices, don’t celebrate quite yet. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although there’s a good chance your answer is correct, it’s possible your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer is wrong, and that the test-maker anticipated your error by 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 including a “ sucker bait” answer choice—just for you and other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test-takers who made the same mistake. (We’ll look at some “ sucker-bait” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 answer choices a few pages ahead.) So check the question to verify that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your response corresponds to what the question calls for—in terms of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value, expression, units of measure, and so forth. If it does, and you’re 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 confident that your work was careful and accurate, don’t spend any more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time checking your work. Confirm your response and move on to the next 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Apply the 5-Step Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It’s time to go back to the three sample questions you looked at a few pages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 back. Let’s walk through them—one at a time–using the 5-step game plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you just learned. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Q uestion 1 is a relatively easy question. Approximately 80% of test-takers 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. If Susan drinks 10% of the juice from a 16-ounce bottle immedi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ately before lunch and 20% of the remaining amount with lunch, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 approximately how many ounces of juice are left to drink after 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 lunch? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 4.8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5.5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 11.2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 11.5 2 12345678901234567890123456789012123456789012345678901 E. 13.0 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: This problem involves the concept of percent—more specifically, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percentage decrease. The question is asking you to perform two 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 computations—in sequence. (The result of the first computation is used to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perform the second one.) Percent questions tend to be relatively simple. All 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that is involved here is a two-step computation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 140 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 2: The five answer choices in this question provide two useful clues: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. N otice that they range in value from 4.8 to 13.0. That’s a broad 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spectrum, isn’t it? But what general value should we be looking 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for in a correct answer to this question? Without crunching any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers, it’s clear that most of the juice will still remain in the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 bottle, even after lunch. So you’re looking for a value much closer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to 13 than to 4. Eliminate (A) and (B). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 2. N otice that each answer choice is carried to exactly one decimal 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 place, and that the question asks for an approx im ate value. These 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two features are clues that you can probably round off your 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 calculations to the nearest “ tenth” as you go. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: You already eliminated (A) and (B) in step 1. But if you’re on your 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 toes, you can eliminate all but the correct answer without resort to precise 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 calculations. Look at the question from a broader perspective. If you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subtract 10% from a number, then 20% from the result, that adds up to a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 bit less than a 30% decrease from the original number. Thirty percent of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 16 ounces is 4.8 ounces. So the solution must be a number that is a bit 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 greater than 11.2 (16 2 4.8). Answer choice (D), 11.5, is the only choice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that fits the bill! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any GM AT Problem Solving questions are designed to reward you for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recognizing easier, more intuitive ways of narrowing down the choices to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the correct answer. Don’t skip over step 3. It’s well worth your time to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 look for a shortcut to the correct answer choice. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: If your intuition fails you, go ahead and crunch the numbers. First, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine 10% of 16, then subtract that number from 16: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 16 3 .1 5 1.6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 16 2 1.6 5 14.4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Susan now has 14.4 ounces of juice. N ow perform the second step. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Determine 20% of 14.4, then subtract that number from 14.4: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 14.4 3 .2 5 2.88 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Round off 2.88 to the nearest tenth: 2.9 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 14.4 2 2.9 5 11.5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 5: The decimal number 11.5 is indeed among the answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Before moving on, however, ask yourself whether your solution makes 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sense—in this case, whether the value of our number (11.5) “ fits” what the 2 2 12345678901234567890123456789012123456789012345678901 1 question asks for. If you performed step 2, you should already realize that 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 141

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 11.5 is in the right ballpark. If you’re confident that your calculations were 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 careful and accurate, confirm your response (D), and move on to the next 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Q uestion 2 is average in difficulty. Approximately 60% of test-takers 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2. The average of 6 numbers is 19. When one of those numbers is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 removed, the average of the remaining 5 numbers is 21. What 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number was taken away? 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 8 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 11 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 20 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: This problem involves the concept of arithm etic m ean (simple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average). To handle this question, you need to be familiar with the formula 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for calculating the average of a series of numbers. But notice that the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question does not ask for the average, but rather for one of the numbers in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the series. This curveball makes the question a bit tougher than most 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 arithmetic mean problems. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Take a quick look at the answer choices for clues. N otice that the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 middle three are clustered closely together in value. So take a closer look at 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two aberrations: (A) and (E). Choice (A) would be the correct answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the question: “ What is the difference between 19 and 21?” But this 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question is asking something entirely different, so you can probably rule 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 out (A) as a sucker bait answer choice. Choice (E) might also be a sucker 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 bait choice, since 20 is simply 19 1 21 divided by 2. If this solution strikes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you as too simple, you’ve got good instincts! The correct answer is 2 2 12345678901234567890123456789012123456789012345678901 probably either (B), (C), or (D). If you’re pressed for time, guess one of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these, and move on to the next question. O therwise, go to step 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In complex questions, don’t look for easy solutions. Problems involving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebraic formulas generally aren’t solved simply by adding (or subtract- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ing) a few numbers. Your instinct should tell you to reject easy answers to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these kind of problems. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 142 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 3: If you’re on your “ intuitive toes,” you might recognize a shortcut 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the answer here. You can solve this problem quickly by simply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 comparing the two sum s. Before the sixth number is taken away, the sum 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 of the numbers is 114 (6 3 19). After removing the sixth number, the sum 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the remaining numbers is 105 (5 3 21). The difference between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sums is 9, which must be the value of the number removed. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Lacking a burst of intuition (step 3), you can solve this problem in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a conventional (and slower) manner. The formula for arithmetic mean 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (simple average) can be expressed this way: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sum of terms in the set 2345678901234567890123456789012123456789012345678901 2 1 AM 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of terms in the set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the question, you started with six terms. Let a through f equal those six 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 terms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a1b1c1d1e1f 2 12345678901234567890123456789012123456789012345678901 19 5 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 114 5 a 1 b 1 c 1 d 1 e 1 f 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 f 5 114 2 ~a 1 b 1 c 1 d 1 e! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Letting f 5 the number removed, here’s the arithmetic-mean formula, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 applied to the remaining five numbers: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a1b1c1d1e 2 12345678901234567890123456789012123456789012345678901 21 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 105 5 a 1 b 1 c 1 d 1 e 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Substitute 105 for (a 1 b 1 c 1 d 1 e) in the first equation: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 f 5 114 2 105 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 f59 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5: If you have time, check to make sure you got the formula right, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and check your calculations. Also make sure you didn’t inadvertently 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 switch the numbers 19 and 21 in your equations. (It’s remarkably easy 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to commit this careless error under time pressure!) If you’re satisfied 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that your analysis is accurate, confirm your answer and move on to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 next question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 143

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Take heed: O n the GM AT, careless errors—such as switching two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers in a problem—is far and away the leading cause of incorrect 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 responses. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 3 is moderately difficult. Approximately 50% of test-takers 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3. If p pencils cost 2q dollars, how many pencils can you buy for c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cents? [N ote: 1 dollar 5 100 cents] 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pc 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2q 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 pc 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 200q 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 50pc 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 q 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2pq 2 12345678901234567890123456789012123456789012345678901 D. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 c 12345678901234567890123456789012123456789012345678901 2 2 E. 200pcq 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 1: The first step is to recognize that this question involves a literal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ex pression. Although it probably won’t be too time-consuming, it may be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a bit confusing. You should also recognize that the key to this question is 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the concept of proportion. It might be appropriate to set up an equation to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solve for c. Along the way, expect to convert dollars into cents. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 2: The five answer choices provide a couple of useful clues: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N otice that each answer choice includes all three letters (p, q, and c). 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 So the solution you’re shooting for must also include all three letters. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • N otice that every answer choice but (E) is a fraction. So anticipate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 building a fraction to solve the problem algebraically. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: Is there any way to answer this question besides setting up an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 algebraic equation? You bet! In fact, there are two ways. O ne is to use easy 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers for the three variables—for example, p 5 2, q 5 1, and c 5 100. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These simple numbers make the question easy to work with: “ If 2 pencils 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cost 2 dollars, how many pencils can you buy for 100 cents?” O bviously, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the answer to this question is 1. Therefore, plug in the numbers into each 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choice to see which choice provides an expression that equals 1. 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 144 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

N ote

Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~2!~100! 2 12345678901234567890123456789012123456789012345678901 O nly choice (B) fits the bill: 5 1. Another way to shortcut the 2 12345678901234567890123456789012123456789012345678901 ~200!~1! 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebra is to apply some intuition to this question. If you strip away the 2 2 12345678901234567890123456789012123456789012345678901 2 pencils, p’s, q’s and c’s, in a very general sense the question is asking: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ If you can by an item for a dollar, how many can you buy for one cent?” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 1 1 2 12345678901234567890123456789012123456789012345678901 Since one cent (a penny) is of a dollar, you can buy of one item for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 100 100 2 12345678901234567890123456789012123456789012345678901 a cent. So you’re probably looking for a fractional answer with a large 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 number in the denominator—something on the order of 100 (as opposed 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to a number such as 2, 3, or 6). Answer choice (B) is the only choice that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 appears to be in the correct ballpark. (B) is indeed the correct answer. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: You can also answer the question in a conventional manner using 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebra. (This is easier said than done.) H ere’s how to approach it: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Express 2q dollars as 200q cents (1 dollar 5 100 cents). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Let x equal the number of pencils you can buy for c cents. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Think about the problem “ verbally,” then set up an equation and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solve for x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ p pencils is to 200q cents as x pencils is to c cents” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The ratio of p to 200q is the same as the ratio of x to c” (in other 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 words, the two ratios are proportionate) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 p x 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 200q c 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 pc 2 12345678901234567890123456789012123456789012345678901 5x 2 12345678901234567890123456789012123456789012345678901 200q 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t worry if you didn’t fully understand the way we set up and solved 2 12345678901234567890123456789012123456789012345678901 2 this problem. You’ll learn more about how to handle GM AT proportion 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions in this book’s math review. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pc 12345678901234567890123456789012123456789012345678901 Step 5: O ur solution, , is indeed among the answer choices. If you 2 2 12345678901234567890123456789012123456789012345678901 200q 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 arrived at this solution using the conventional algebraic approach (step 4), 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you can verify your solution by substituting simple numbers for the three 2 12345678901234567890123456789012123456789012345678901 variables (as we did in step 3). O r, if you arrived at your solution by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plugging in numbers, you can check your work by plugging in a different 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set of numbers or by thinking about the problem conceptually (as in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 step 3). O nce you’re confident you’ve chosen the correct expression among 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 145

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the five choices, confirm your choice, and then move on to the next 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. The correct answer is indeed B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for GMAT Problem Solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are some basic tips you should follow for any type of Problem 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 Solving question. Apply these “ keys” to Part V’s practice tests, and then 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 review them again just before exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Narrow Down Answer Choices Up Front by Sizing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Up the Question 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 If the question asks for a number value, you can probably narrow down 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the answer choices by estimating the value and type of number you’re 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 looking for. Use your common sense and real-world experience to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formulate a “ ballpark” estimate for word problems. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 You can narrow down answer choices by looking at the problem from a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ common sense” viewpoint. The five answer choices in this question 2 2 12345678901234567890123456789012123456789012345678901 provide some useful clues. N otice that they range in value from 4.8 to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13.0. That’s a wide spectrum, isn’t it? But what general value should you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be looking for in a correct answer to this question? Without crunching any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers, it’s clear that most of the juice will still remain in the bottle, even 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 after lunch. So you’re looking for a value much closer to 13 than to 4. So 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you can safely eliminate (A) and (B). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Common Sense Can Sometimes Reveal the Right 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answer 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In many questions, you can eliminate all but the correct answer without 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 resorting to precise calculations. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Look at the question from a broader perspective. If you subtract 10% 2 2 12345678901234567890123456789012123456789012345678901 from a number, then 20% from the result, that adds up to a bit less than a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 30% decrease from the original number. Thirty percent of 16 ounces is 4.8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ounces. So the solution must be a number that is a bit greater than 11.2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (16 2 4.8). Choice (D), 11.5, is the only choice that fits the bill! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In Q uestion 3, notice that c is a much greater number than either p or q. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nly a fraction with c in the numerator and a large number in the denomi- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 146 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 nator (or vice versa) is likely to yield a quotient you’re looking for. With this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in mind, choice (B) jumps off the paper at you as the likely choice! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Scan the Answer Choices for Clues to Solving the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Scan the answer choices to see what all or most of them have in common— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 such as radical signs, exponents, factorable expressions, or fractions. Then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 try to formulate a solution that looks like the answer choices. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 3 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 N otice that each answer choice includes all three letters (p, q, and c). So the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution you’re aiming for must also include all three letters. Also, notice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that every answer but choice (E) is a fraction. So, anticipate building a 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 fraction to solve the problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Be Reeled in by Too-Obvious, Sucker-Bait 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Answer Choices 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The test-makers will intentionally tempt or “ bait” you with wrong-answer 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices that result from making common errors in calculation and in set- 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ting up and solving equations. Don’t assume that your response is correct 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 just because your solution appears among the five answer choices! Rely 2 2 12345678901234567890123456789012123456789012345678901 instead on your sense for whether you understood what the question called 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for and performed the calculations and other steps carefully and accurately. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this question, each of the four incorrect choices is sucker bait: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4.8 You performed the wrong calculation: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 30% of 16 ounces 5 4.8 ounces 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5.5 This is the number of ounces Susan drank. (The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question asks for the amount remaining.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 11.2 You performed the wrong calculation: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 30% of 16 ounces 5 4.8 ounces 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 16 2 4.8 5 11.2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 11.5 This is the correct answer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 13.0 You confused percentages with raw numbers, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 erroneously converting 30% (10% 1 20% ) into 3.0: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 16 2 3.0 5 13.0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 147

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This question contains two sucker bait answer choices: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 2 This would be the correct answer to the question: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ What is the difference between 19 and 21?” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 But this question is asking something entirely different. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 20 20 is simply 19 1 21 divided by 2. If this solution 2345678901234567890123456789012123456789012345678901 2 1 strikes you as too simple, you’ve got good instincts! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Don’t do More Work Than Needed to Get to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answer 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the question asks for an approximation, that’s a huge clue that precise 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculations aren’t necessary. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 Question 1 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that each answer choice is carried to exactly one decimal place, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the question asks for an approximate value. These two features are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clues that you can probably round off your calculations to the nearest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tenth as you go. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Look for Shortcuts to Conventional Ways of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solving Problems 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The adage “ There’s more than one way to skin a cat” applies to many 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Problem Solving questions. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can solve this problem quickly by simply comparing the two sum s. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Before the sixth number is removed, the sum of the numbers is 114 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (6 3 19). After removing the sixth number, the sum of the remaining 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers is 105 (5 3 21). The difference between the two sums is 9, which 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must be the value of the number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Know When to Plug in Numbers for Variables 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the answer choices contain variables (like x and y), the question might be 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 a good candidate for the “ plug-in” strategy. Pick simple numbers (so the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 math is easy) and substitute them for the variables. You’ll definitely need 2 2 12345678901234567890123456789012123456789012345678901 your pencil for this strategy. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 148 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This question was a perfect candidate for the plug-in strategy. Instead of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trying to figure out how to set up and solve an algebraic equation, in step 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 3 we used easy numbers for the three variables, then plugged those 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers into each answer choice to see which choice worked. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Know When to Work Backward from Numerical 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Answer Choices 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a Problem Solving question asks for a number value, and if you draw a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 blank as far as how to set up and solve the problem, don’t panic. You 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 might be able work backward by testing each answer choice. This might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 take a bit of time, but if you test the answer choices in random order, the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 statistical odds are that you’ll only need to test three choices to find the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct one. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You already learned that comparing the two sums is the quickest shortcut 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to the answer. But if this strategy didn’t occur to you, working backward 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from the answer choices would be the next quickest method. After the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sixth number is removed, the sum of the five remaining numbers is 21 3 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 105. So, to test an answer choice, add this sum to the number provided 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in the choice, dividing the new sum by 6. If the result is 19, you’ve found 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the correct choice. H ere’s how to do the math for choice (C), which is the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct answer choice: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 105 1 9 114 2 12345678901234567890123456789012123456789012345678901 5 5 19 2 12345678901234567890123456789012123456789012345678901 6 6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving questions always list numerical answer choices in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ascending order of value. So, if you use the strategy of working backward, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 start with the median value: choice (C). If (C) turns out too great, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know the correct answer must be either (A) or (B). Conversely, if (C) turns 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 out too small valued, then either (D) or (E) must be correct. O f course, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you might also be able to eliminate an answer choice right away by sizing 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 up the questions (a previous strategy). Doing so would make your job 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 even quicker! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 149

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Always Check Your Work 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Always check your work. H ere are three suggestions for doing so: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Do a reality check. Ask yourself whether your solution makes 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sense based upon what the question asks. (This check is especially 2 2 12345678901234567890123456789012123456789012345678901 2 appropriate for word problems.) 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. For questions where you solve algebraic equations, plug your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution into the equation(s) to make sure it works. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3. Confirm your calculations (except for the simplest no-brainers) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with your calculator. It’s amazingly easy to accidentally push the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 wrong button. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Checking your calculations is especially crucial for questions asking for 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an approximation. Why? If your solution doesn’t precisely match one of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the five answer choices, you might conclude that you should just pick the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choice that’s closest to your solution—a big mistake if you miscalculated! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A reality check on this question will tell you that answer choice (C), 11.5, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 seems about right, but that most of the other choices don’t. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Read the Question One Last Time before 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Moving on 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Among GM AT test-takers, simple carelessness in reading a Problem 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solving question is by far the most likely cause of an incorrect answer. So 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 even if your solution is among the choices, and you’re confident your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 calculations are accurate, don’t move on quite yet. Read the question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 again. M ake sure you answered the precise question asked. For example, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 does the question ask for: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Arithmetic mean or median? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A circumference or an area? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A sum or a difference? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A perimeter or a length of one side only? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • An aggregate rate or a single rate? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Total time or average time? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 150 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 4: Problem Solving

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Also check to make sure you: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Used the same numbers provided in the question 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Didn’t inadvertently switch any numbers or other expressions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Didn’t use raw numbers where percentages were provided, or 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 vice-versa 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 1 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The question asked for the amount of juice remaining, not the amount 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Susan drank. Also, a careless test-taker might subtract 10 ounces instead 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 of 10% . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A careless test-taker might inadvertently switch the numbers 19 and 21. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The question asks for an answer in cents, not dollars. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 151

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level of GM AT Problem Solving. At this point, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you’ll: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Apply the success keys you learned earlier to more challenging 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Problem Solving questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn additional success keys that apply to certain types of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem Solving questions, and apply these keys to example 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll explore some of the strategies you learned 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 earlier in this chapter—applying them to GM AT-style questions that are a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bit more challenging. You’ll also learn some additional strategies that 2 2 12345678901234567890123456789012123456789012345678901 apply to certain types of Problem Solving questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Scan the Answer Choices for Clues to Solving the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problem 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Scan the answer choices to see what all or most of them have in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 common—such as radical signs, exponents, factorable expressions, or 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fractions. Then, try to formulate a solution that looks like the answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 152

Chapter 4: Problem Solving

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 If a Þ 0 or 1, then 5 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 2 12345678901234567890123456789012123456789012345678901 22 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2a 2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 a22 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 a22 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 D. 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2a 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. N otice what all the answer choices have in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 common: Each one is a fraction in which the denominator contains the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 variable a. And, there are no fractions in either the numerator or the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 denominator. That’s a clue that your job is to manipulate the expression 2 12345678901234567890123456789012123456789012345678901 given in the question so that the result includes these features. First, place 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the denominator’s two terms over the common denominator a. Then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 divide a from the denominators of both the numerator fraction and the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 denominator fraction (this is a shortcut to multiplying the numerator 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fraction by the reciprocal of the denominator fraction): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a a 1 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2a 2 2 2a 2 2 2 12345678901234567890123456789012123456789012345678901 22 2 12345678901234567890123456789012123456789012345678901 a a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use Common-Sense “Guesstimates” to 2 12345678901234567890123456789012123456789012345678901 2 1 Narrow the Field—But Know the Limits of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This Strategy 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 If the question asks for a numerical value, you can probably narrow down 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the answer choices by estimating the value and type of number you’re 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 looking for. Use your common sense and real-world experience to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formulate a “ ballpark” estimate for word problems. But keep in mind: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t expect to eliminate all answer choices but the correct one by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 common sense alone. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 153

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A spinner containing seven equal regions numbered 1 through 7 is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spun two times in a row. What is the probability that the first spin 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yields an odd number and the second spin yields an even number? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 49 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 2 14 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 7 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. This problem involves the concept of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 probability. Common sense about basic probability should tell you that, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with odds of close to 50% of spinning the desired type of number on each 2 2 12345678901234567890123456789012123456789012345678901 of the two spins, the odds of spinning such a number twice in a row should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be less than 50% . So, you can eliminate choices (D) and (E). Your odds of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answering the question correctly are now 1 in 3. But notice that the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remaining choices—(A), (B), and (C)—are closely grouped in value. Also 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 notice that, in each of these remaining choices, the denominator contains 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the sort of number you could end up with when you apply a mathematical 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 operation to the numbers given in the question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: You’ve probably reached the limits of applying common 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense, and you’ll need to solve the problem mathematically to find the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct choice. H ere’s how to do it. There are four odd numbers (1, 3, 5, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and 7) and three even numbers (2, 4, and 6) on the spinner. So, the chances 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 12345678901234567890123456789012123456789012345678901 of yielding an odd number with the first spin are 4 in 7, or . The chances 2 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 of yielding an even number with the second spin are 3 in 7, or . To 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine the probability of both events occurring, combine the two 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 individual probabilities by multiplication: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 3 12 2 12345678901234567890123456789012123456789012345678901 3 5 2 12345678901234567890123456789012123456789012345678901 7 7 49 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 154 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 4: Problem Solving

Take It to the Next Level

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N otice the sucker-bait answer choice in this question: Answer choice (D) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 3 2 12345678901234567890123456789012123456789012345678901 provides the simple average of the two individual probabilities: and . 2345678901234567890123456789012123456789012345678901 2 1 7 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 Aside from the fact that , or 50% , is too high a probability from a 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 common-sense viewpoint, should strike you as too easy a solution to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what appears to be a complex problem. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 Know When to Plug in Numbers for Variables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 If the answer choices contain variables (like x and y), the question might be 2 2 12345678901234567890123456789012123456789012345678901 a good candidate for the “ plug-in” strategy. Pick simple numbers (so the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 math is easy), and substitute them for the variables. You’ll definitely need 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your pencil for this strategy. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If a train travels r 1 2 miles in h hours, which of the following repre- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sents the number of miles the train travels in 1 hour and 30 minutes? 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3r 1 6 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2h 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3r 2 12345678901234567890123456789012123456789012345678901 B. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 h12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 r12 2 12345678901234567890123456789012123456789012345678901 C. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 h13 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 r 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 h 1 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 E. ~r 1 2! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. This is an algebraic word problem involving 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 rate of motion (speed). You can solve this problem either conventionally or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by using the plug-in strategy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 T he conventional w ay: N otice that all of the answer choices contain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fractions. This is a clue that you should try to create a fraction as you solve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the problem. H ere’s how to do it. Given that the train travels r 1 2 miles in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 r12 3 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 h hours, you can express its rate in miles per hour as . In hours, the 2 2 12345678901234567890123456789012123456789012345678901 h 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 train would travel this distance: 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3r 1 6 3 r12 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 h 2h 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 155

S DS D

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 T he plug-in strategy: Let r 5 8 and h 5 1. Given these values, the train 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 travels 10 miles (8 1 2) in 1 hour. O bviously, in 1 hours the train will 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 travel 15 miles. Start plugging these r and h values into the answer choices. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You won’t need to go any further than choice (A): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3r 1 6 3~8! 1 6 30 2 12345678901234567890123456789012123456789012345678901 2 5 5 , or 15 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2h 2~1! 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Even if you had no clue how to handle this question, you could at least 2 12345678901234567890123456789012123456789012345678901 2 eliminate choice (E) out of hand. It omits h! Common sense should tell 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you that the correct answer must include both r and h. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 Know When to Work Backward from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Numerical Answer Choices 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a Problem Solving question asks for a number value, and if you draw a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 blank as far as how to set up and solve the problem, don’t panic. You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might be able to work backward by testing the answer choices, each one in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 turn. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A ball is dropped 192 inches above level ground, and after the third 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bounce, it rises to a height of 24 inches. If the height to which the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ball rises after each bounce is always the same fraction of the height 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reached on its previous bounce, what is this fraction? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 8 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 D. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The fastest route to a solution is to plug in an 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 answer. Try choice (C), and see what happens. If the ball bounces up as 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 high as it started, then after the first bounce it will rise up as high as 192 2 12345678901234567890123456789012123456789012345678901 2 1 3 2 156 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 4: Problem Solving

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 inches, or 64 inches. After a second bounce, it will rise as high, or about 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 21 inches. But, the problem states that the ball rises to 24 inches after the 2 2 12345678901234567890123456789012123456789012345678901 third bounce. O bviously, if the ball rises less than that after two bounces, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it’ll be way too low after three. So, choice (C) cannot be the correct answer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 We can see that the ball must be bouncing higher than one third of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way; so the correct answer must be a greater fraction, either choice (D) or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice (E). You’ve already narrowed your odds to 50% . Try plugging in 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 1 1 1 2 2 12345678901234567890123456789012123456789012345678901 choice (D), and you’ll see that it works: of 192 is 96; of 96 is 48; and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 2 2 2345678901234567890123456789012123456789012345678901 2 1 of 48 is 24. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although it would be possible to develop a formula to answer the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question, doing so would be senseless, considering how quickly and easily 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you can work backward from the answer choices. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Know When Not to Work Backward from 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Numerical Answer Choices 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Working backward from numerical answer choices works well when the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers are easy, and when few calculations are required, as in the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 preceding question. In other cases, applying algebra might be a better way. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ow many pounds of nuts selling for 70 cents per pound must be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mixed with 30 pounds of nuts selling at 90 cents per pound to make 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a mixture that sells for 85 cents per pound? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 12 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 15 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 20 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 24 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. Is the easiest route to the solution to test the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choices? Let’s see. First of all, calculate the total cost of 30 pounds 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of nuts at 90 cents per pound: 30 3 .90 5 $27. N ow, start with choice (C). 2 12345678901234567890123456789012123456789012345678901 15 pounds of nuts at 70 cents per pound costs $9.50. The total cost of this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mixture is $36.50, and the total weight is 45 pounds. N ow you’ll need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perform long division. The average weight of the mixture turns out to be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between 81 and 82 cents—too small valued for the 85 cent average given 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the question. At least you can eliminate choice (C). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You should realize by now that testing the answer choices might not be the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 most efficient way to tackle this question. Besides, there are ample 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 157

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 opportunities for calculation errors. Instead, try solving this problem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebraically—by writing and solving a system of equations. H ere’s how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to do it. The cost (in cents) of the nuts selling for 70 cents per pound can be 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 expressed as 70x , letting x equal the number that you’re asked to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine. You then add this cost to the cost of the more expensive nuts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (30 3 90 5 2,700) to obtain the total cost of the mixture, which you can 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 express as 85(x 1 30). You can state this algebraically and solve for x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as follows: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 70x 1 2,700 5 85~x 1 30! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 70x 1 2,700 5 85x 1 2,550 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 150 5 15x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 5 x 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 pounds of 70-cent-per-pound nuts must be added in order to make a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mixture that sells for 85 cents per pound. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Avoid Heavy Lifting; Look for the Easiest 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Route to the Answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the question asks for an approximation, then you know that precise 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculations won’t be necessary, and you can safely “ round off” the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers as you go. But, even in other questions, you can sometimes 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eliminate all but the correct answer without resort to precise calculations. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What is the difference between the sum of all positive even integers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 less than 102 and the sum of all positive odd integers less than 102? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 50 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 51 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 101 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. To see the pattern, compare the initial terms of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each sequence: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 even integers: {2,4,6, . . . 100} 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 odd integers: {1,3,5, . . . , 99,101} 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that, for each successive term, the odd integer is one less than the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 corresponding even integer. There are a total of 50 corresponding integers, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 so the difference between the sums of all these corresponding integers is 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 50. But the odd-integer sequence includes one additional integer: 101. So 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the difference is (250 1 101), or 51. 2 1 2 158 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 4: Problem Solving

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 If 112345678901234567890123456789012123456789012345678901 a Geometry Problem Provides a Figure, 2345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Mine it for Clues 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 M ost geometry problems are accompanied by figures. They’re there for a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reason! The pieces of information a figure provides can lead you, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 step-by-step, to the answer. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If O is the center of the circle in the figure above, what is the area 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the shaded region, expressed in square units? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 A. p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. 2p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 C. 2 12345678901234567890123456789012123456789012345678901 p 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 p 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 3p 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. This question asks for the area of a portion of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the circle defined by a central angle. To answer the question, you’ll need to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine the area of the entire circle as well as what percent (portion) of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that area is shaded. This multi-step question is as complex as any you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 might encounter on the GM AT. But there’s no need to panic; just start with 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 what you know, then move step-by-step toward the answer. M ine the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 figure for a piece of information that might provide a starting point. 2 2 12345678901234567890123456789012123456789012345678901 DO CD is your first “ stepping stone.” H ere are the steps to the answer: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You know that O C and O D are congruent (equal in length) because 2 12345678901234567890123456789012123456789012345678901 each one is the circle’s radius. In any triangle, angles opposite 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 159

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 congruent sides are also congruent (the same size, or degree measure). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, ∠O D C must measure 60°—just like ∠O CD . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For any triangle, the sum of the measures of all three interior angles is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 180°. Thus, ∠CO D measures 60°, just like the other two angles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Vertical angles created by two intersecting lines are congruent. Thus, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ∠A O B also measures 60°. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 By the same reasoning as in steps 1 and 2, each angle of DA BO measures 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A B is given as 3. Accordingly, the length of 60°. N otice that the length of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each and every side of both triangles is 3. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Since this length (3) is also the circle’s radius (the distance from its center 2 2 12345678901234567890123456789012123456789012345678901 to its circumference), you can determine the circle’s area. The area of any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle is pr2 , where r is the circle’s radius. Thus, the area of the circle is 9p. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow determine what portion of the circle’s area is shaded. The four angles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formed at the circle’s center (O ) total 360°. You know that two of these 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 angles account for 120°, or of those 360°. ∠A O C is supplementary to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 ∠D O C ; that is, the two angles combine to form a straight line, and so 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their measures total 180°. Therefore, ∠A O C measures 120°. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 120° is of 360°. Thus, the shaded portion accounts for the circle’s area, 2 12345678901234567890123456789012123456789012345678901 3 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or 3p. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you look at the 60° angle in the figure, you might recognize right away 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that both triangles are equilateral and, extended out to their arcs, form 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 two “ pie slices,” each one the size of the whole “ pie” (the circle). What’s 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 left are two big slices, each of which is twice the size of a small slice. So the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 shaded area must account for the circle’s area. With this intuition, the 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem is reduced to the simple mechanics of calculating the circle’s 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 area, then dividing it by 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 160 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 4: Problem Solving

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 If 112345678901234567890123456789012123456789012345678901 A Geometry Problem Doesn’t Provide A 2345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Figure, Sketch One 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A geometry problem that does not provide a diagram might cry out for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one. That’s your cue to take pencil to scratch paper and draw one yourself. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A rancher uses 64 feet of fencing to create a rectangular horse 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corral. If the ratio of the corral’s length to width is 3:1, which of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following most closely approximates the minimum length of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 additional fencing needed to divide the rectangular corral into three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangular corrals, one of which is exactly twice the area of the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 other two? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 24 feet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 29 feet 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 36 feet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 41 feet 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 48 feet 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is B. Your first step is to determine the dimensions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the rectangular corral. Given a 3:1 length-to-width ratio, you can solve 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for the width (w ) of the field using the perimeter formula: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2~3w ! 1 2~w ! 5 64 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 8w 5 64 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w 58 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Accordingly, the length of the rectangular corral is 24 feet. N ext, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 determine how the rancher must configure the additional fencing to meet 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the stated criteria. This calls for a bit of sketching to help you visualize the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 dimensions. O nly two possible configurations create three triangular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corrals with the desired ratios: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 161

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The top figure requires less fencing. You can determine this fact by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculating each length (using the Pythagorean theorem). O r you can also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use logic and visualization. H ere’s how. As a rectangle becomes flatter 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 (“ less square” ), the shorter length approaches zero (0), at which point the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 minimum amount of fencing needed in the top configuration would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decrease, approaching the length of the longer side. H owever, in the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 bottom design, the amount of fencing needed would increase, approaching 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 twice the length of the longer side. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Your final step is to calculate the amount of fencing required by the top 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 design, applying the Theorem (let x 5 either length of cross-fencing): 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 2 12345678901234567890123456789012123456789012345678901 8 1 12 5 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 64 1 144 5 x 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 208 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 5 =208 ' 14.4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, a minimum of approximately 28.8 feet of fencing is needed. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answer choice (B) approximates this solution. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Since the question asks for an approximation, it’s a safe bet that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 estimating =208 to the nearest integer will suffice. If you learned your 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ times table,” you know that 14 3 14 5 196, and 15 3 15 5 225. So 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 =200 must be between 14 and 15. That’s close enough to zero in on 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice (B), which provides twice that estimate. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 To112345678901234567890123456789012123456789012345678901 Handle “Defined Operation” Questions, 2345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Just Plug in the Numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 At least one of your 25–26 Problem Solving questions will probably be an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 example of what’s called a “ defined operation.” These questions look 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weird and therefore might strike you as difficult. But they’re really not. In 2 2 12345678901234567890123456789012123456789012345678901 fact, the math turns out to be ridiculously easy. What’s being tested is your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ability to understand what the problem requires, and then to perform the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simple arithmetical calculations, carefully! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 162 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 4: Problem Solving

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 b b 2 12345678901234567890123456789012123456789012345678901 a c a c Let be defined for all numbers a, b, c, and d by 5 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 d d 4 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 5 2 , what is the value of x 2 ? ac 2 bd. If x 5 2 12345678901234567890123456789012123456789012345678901 1 1 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 C. 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 38 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 178 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is B. In defining the diamond-shaped figure as 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ ac 2 bd,” the test-makers are saying that whenever you see four numbers 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 in a diamond like this, you should plug them into the mathematical 2 2 12345678901234567890123456789012123456789012345678901 expression shown in the order given. The question itself then requires you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to perform this simple task twice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 First, let’s figure out the value of x . If x is the diamond labeled as x , then a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5, b 5 4, c 5 2, and d 5 1. N ow, we plug those numbers into the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 equation given, and do the simple math: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 5 ~5 3 2! 2 ~4 3 1! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 510 2 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 56 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, we tackle the second step. H aving figured out the value of x , we can 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 plug it into our second diamond, where a 5 6, b 5 10, c 5 2, and d 5 1. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Again, plug in the numbers and do the math: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (6 3 2) 2 (10 3 1) 5 12 2 10 5 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 As you can see, the math is very easy; the trick is understanding what the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 test-makers are doing, which is “ defining” a new math operation, and then 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 carefully plugging in the numbers and working out the solution. With a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 little practice, you’ll never get a “ defined operation” question wrong. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 163

Chapter

5 Data Sufficiency

164

N ote

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to GM AT Data Sufficiency. At this point, you’ll learn the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A step-by-step approach to handling any Data Sufficiency question 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Success keys for tackling Data Sufficiency questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency—Your 5-Step Game Plan 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The first task in this chapter is to learn the five basic steps for handling a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 GM AT Data Sufficiency question. You’ll apply these steps to the following 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four sample questions. At the risk of giving away the answers up front, the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 correct answer is different for each question. Take a minute or two to 2 2 12345678901234567890123456789012123456789012345678901 attempt each one. (We’ll analyze all four questions a few pages ahead.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 We’ve labeled the answer choices here A through E. Remember, however, 2 2 12345678901234567890123456789012123456789012345678901 that on the actual GM AT CAT screen, you’ll select your choice by clicking 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on one of five blank ovals (instead of lettered answer choices). But the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices themselves will always be exactly the same (and in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same order) as A through E here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 5: Data Sufficiency

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Sample Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. If a jewelry merchant bought a particular ring for $10,000 and sold 12345678901234567890123456789012123456789012345678901 2 2 the ring to Judith, how much did Judith pay for the ring? 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) The merchant’s profit from the sale was 50% . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) The amount that the merchant paid for the ring was two-thirds 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the amount that Judith paid for the ring. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Statement (1) ALO N E is sufficient, but statement (2) alone is 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Statement (2) ALO N E is sufficient, but statement (1) alone is 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 N O T sufficient to answer the question asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 2 12345678901234567890123456789012123456789012345678901 answer the question asked, but N EITH ER statement ALO N E 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is sufficient. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Each statement ALO N E is sufficient to answer the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 asked. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 problem are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The symbol N represents the third digit in the 5-digit number 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 62,N79. What number does N represent? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (1) 62,N79 is a multiple of 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (2) The sum of the digits of 62,N79 is divisible by 4. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. Statement (1) ALO N E is sufficient, but statement (2) alone is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. Statement (2) ALO N E is sufficient, but statement (1) alone is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 answer the question asked, but N EITH ER statement ALO N E 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is sufficient. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. Each statement ALO N E is sufficient to answer the question 2 12345678901234567890123456789012123456789012345678901 asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 problem are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 165

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. If x y Þ 0, is x . y? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) |x | . |y| 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) x 5 2y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Statement (1) ALO N E is sufficient, but statement (2) alone is 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 N O T sufficient to answer the question asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Statement (2) ALO N E is sufficient, but statement (1) alone is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 2 12345678901234567890123456789012123456789012345678901 2 answer the question asked, but N EITH ER statement ALO N E 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is sufficient. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. Each statement ALO N E is sufficient to answer the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 asked. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 problem are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the figure above, is A B equal in length to A C? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) x 1 y 5 z 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) y 5 180 2 z 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. Statement (1) ALO N E is sufficient, but statement (2) alone is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. Statement (2) ALO N E is sufficient, but statement (1) alone is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N O T sufficient to answer the question asked. 12345678901234567890123456789012123456789012345678901 2 2 C. BO TH statements (1) and (2) TO GETH ER are sufficient to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question asked, but N EITH ER statement ALO N E 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is sufficient. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Each statement ALO N E is sufficient to answer the question 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 asked. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Statements (1) and (2) TO GETH ER are N O T sufficient to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 answer the question asked, and additional data specific to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem are needed. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 166 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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N ote

Chapter 5: Data Sufficiency

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Some Data Sufficiency questions will include diagrams (geometry figures, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 graphs, and charts), but most won’t. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The 5-Step Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the 5-step approach that will help you to handle any Data 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Sufficiency question. Just a few pages ahead, we’ll apply this approach to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four sample Data Sufficiency questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Step 1: Size up the question first. As with Problem Solving questions, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assess what specific mathematical area is being tested (e.g., what 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mathematical rules and formulas come into play). By determining what 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you’re up against, you’re well on your way to dealing with the question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Data Sufficiency questions, just like Problem Solving questions, vary 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 widely in difficulty level. Try to get a feel for your limitations in handling 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 complex questions. Determine how much time you’re willing to spend on 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the question, if any. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Size up the two statements and look for a shortcut to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct answer. Before you plunge into a full-blown analysis of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement (1), read both statements and ask yourself: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Do the statements provide essentially the same information? If so, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the answer is probably either choice (D) or choice (E). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Does either statement establish a solvable system of equations (for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 example, two equations in two variables)? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Does a statement seem to merely repeat (paraphrase) all or some 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the information in the question? (If so, you can’t answer the 2 12345678901234567890123456789012123456789012345678901 question with that statement alone.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Asking yourself questions such as these may in some cases enable you to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 determine the correct answer choice without doing any more work. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O therwise, proceed to step 3. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3. Consider statement (1) alone. If the information provided in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 statement (1) suffices to answer the question, eliminate choices (B), (C), 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and (E) as viable answer choices. O n the other hand, if statement (1) is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 insufficient alone, eliminate choices (A) and (D) as viable answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you’re pressed for time, after step 3, take your best guess and move on. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your odds of selecting the correct answer choice are pretty good at 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 this point. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 167

Part III: Q uantitative A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 4. Consider statement (2) alone. If the information provided in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement (2) suffices to answer the question, eliminate choices (A), (C), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and (E) as viable answer choices. O n the other hand, If statement (2) is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 insufficient alone, eliminate choices (B) and (D) as viable answer choices. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5. If neither statement alone suffices to answer the question, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 consider both statements together. N ow if you can answer the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question, the correct answer choice is (C). If you still don’t have enough 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information, the correct answer choice is (E). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Apply the 5-Step Plan 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 It’s time to go back to the three sample questions you looked at a few pages 2 2 12345678901234567890123456789012123456789012345678901 back. Let’s walk through them—one at a time—using the 5-step game plan 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you just learned. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 By now you’re probably familiar with the five answer choices, so we 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t bother including them with the questions from now on. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Q uestion 1 is a relatively easy question. Approximately 85% of test-takers 2 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. If a jewelry merchant bought a particular ring for $10,000 and sold 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the ring to Judith, how much did Judith pay for the ring? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) The merchant’s profit from the sale was 50% . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) The amount that the merchant paid for the ring was two-thirds 2 12345678901234567890123456789012123456789012345678901 of the amount that Judith paid for the ring. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: The focus of this question is the concept of percent increase—in 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the context of a word problem involving profit. This type of question is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 usually fairly easy, so you can expect to determine the correct response 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 within a minute—without resorting to an educated guess. It should be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 worth investing your time on this one. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: N otice that the two statements (1 and 2) provide the same 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information—only in different ways! This is a huge clue that the correct 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choice is either (D) or (E). You’ll still have to consider one of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two statements alone, but that should suffice. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 3: Consider the premise, along with statement (1) alone. (Disregard 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement (2) for now.) Given that the merchant paid $10,000 for the ring, 2 12345678901234567890123456789012123456789012345678901 2 1 2 168 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 5: Data Sufficiency

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 if the merchant earned a 50% profit from the sale to Judith, determining 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Judith’s ring price is a simple matter of adding 50% of $10,000 to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $10,000: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 $10,000 1 .5($10,000) 5 Judith’s ring price 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 At this point, it’s clear that you can determine Judith’s ring price by simple 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 multiplication and addition. Don’t waste time actually computing Judith’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ring price. You know that statement (1) alone suffices to answer the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 question and that’s all you need to know! Eliminate choices (B), (C), and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (E) from consideration. The correct choice must be either (A) or (D). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: If you’re not convinced that both statements say essentially the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 same thing, go ahead and consider the premise along with statement (2) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 alone. (Disregard statement (1) for now.) If the merchant’s cost was the 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 of the merchant’s cost. 2 amount Judith paid, then Judith paid 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Determining Judith’s ring price is a simple matter of multiplying $10,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 by : 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $10,000 3 5 Judith’s ring price 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 At this point, it’s clear that you can determine Judith’s ring price by simple 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 multiplication. As in step 3, don’t waste time actually computing that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 price. You know that statement (2) alone suffices to answer the question 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and that’s all you need to know! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 5: This step is unnecessary here. There’s no need to consider both 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 statements together. You know that either statement (1) or (2) alone 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suffices to answer the question, so you can eliminate choices (C) and (E). 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer must be D. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 2 is average in difficulty level. Approximately 65% of test-takers 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The symbol N represents the third digit in the 5-digit number 2 12345678901234567890123456789012123456789012345678901 62, N79. What number does N represent? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (1) 62, N79 is a multiple of 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (2) The sum of the digits of 62, N79 is divisible by 4. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 169

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 1: This question is testing on factors and divisibility. The peculiar use 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of a “ placeholder” is a typical GM AT technique for testing your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 understanding of integers and digits. Q uestions such as these are usually 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 straightforward once you know the basic rules as well as a few shortcuts 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for divisibility. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Step 2: Both statements appear to add different information to the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. So there’s no obvious shortcut here. (Go on to step 3.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Step 3: Consider statement (1) alone. If the sum of the digits of a number 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is divisible by 3, the number is also divisible by 3. Excluding the digit 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 represented by N, the sum of the digits in the number 62, N79 is 24. 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Accordingly, if the number is a multiple of (divisible by) 3, the missing digit 2 2 12345678901234567890123456789012123456789012345678901 must be 0, 3, 6, or 9. Since there’s more than one possible value for N, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement (1) alone is insufficient to answer the question. Eliminate answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices (A) and (D). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Consider statement (2) alone. The number that N represents can be 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 0, 4, or 8. Thus, statement (2) alone is insufficient to answer the question. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Eliminate answer choice (B). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5: Consider statements (1) and (2) together. The two statements 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 together establish that the missing digit is 0, because 0 is the only common 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number in between the two lists of possible values for N. Thus, statements 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (1) and (2) together are sufficient to answer the question, and the correct 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 answer choice is (C). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Q uestion 3 is moderately difficult. Approximately 45% of test-takers 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. If x y Þ 0, is x . y? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) |x | . |y| 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) x 5 2y 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: This is a typical absolute value question. Whenever you see 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 inequalities and variables but no numbers, that’s a clue that you’ll need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 consider different types of numbers—such as negative numbers, positive 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbers, fractions, and perhaps the numbers 0 and 1—to determine the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 correct answer choice. Getting to the answer might entail performing some 2 2 12345678901234567890123456789012123456789012345678901 simple calculations, and perhaps a bit of trial and error (plugging in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible values). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Both statements appear to add different information to the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question. So there’s no obvious shortcut here. But a good reasoned guess at 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 170 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 this point would be that the correct answer choice is (E). Why? Because the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question doesn’t restrict the value of either x or y (except that neither can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equal 0). So if you’re pressed for time, guess choice (E) and move on to the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 next question. O therwise, go on to step 3. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: You must consider both positive and negative values for x and y. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Given |x | . |y|, an x -value of either 4 or 24 and a y-value of 2, for example, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 satisfies the inequality but results in two different answers to the question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, statement (1) alone is insufficient to answer the question. Eliminate 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 answer choices (A) and (D). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Step 4: Similarly, given x 5 2y, if you use negative values for both x and y 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 (for example, x 5 24 and y 5 22), the answer to the question is no; but if 2 2 12345678901234567890123456789012123456789012345678901 you use positive values (for example, x 5 4 and y 5 2), the answer to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question is yes. Thus, statement (2) alone is insufficient. Eliminate answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice (B). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5: Statements (1) and (2) together are still insufficient. For example, 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 if x 5 24 and y 5 22, both statements (1) and (2) are satisfied, x , y, and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the answer to the question is no. H owever, if x 5 4 and y 5 2, statements 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (1) and (2) are both satisfied, but x . y, and the answer to the question is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yes. Eliminate answer choice (C). The correct answer must be E. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 4 is a relatively difficult question. Approximately 30% of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 test-takers respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the figure above, is A B equal in length to A C? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) x 1 y 5 z 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) y 5 180 2 z 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 1: This question is a geom etry problem involving the isosceles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 triangle. (You’ll see anywhere from five to eight geometry questions on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your GM AT CAT.) This question involves three distinct rules of geometry. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Two of these rules (A and C below) apply specifically to triangles: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 R ule A : If two angles of a triangle are congruent, then the two sides 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opposite those angles are congruent. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 171

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 R ule B: If angles formed from the same vertex form a straight line, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their degree measures total 180 (and they are known as “ supplemen- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tary” angles). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 R ule C: In any triangle, the sum of the degree measures of the three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interior angles is 180. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 If you’re unfamiliar with any of the three rules in step 1, you won’t get very 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 far with this question! So if you’re pressed for time, and if you’re 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 particularly weak in this area of geometry, consider taking a guess and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 moving on. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Intuition alone probably won’t get you very far on this question. If 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you’re really on your toes, you’ll notice that statement (1) merely restates 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Rule C (see step 1) in a different form. Also, because statement (2) includes 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a number, this statement is probably more likely than statement (1) to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suffice in answering the question. (This amounts to little more than a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 guess, however.) So let’s move on to step 3. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t shortcut the analysis by simply measuring the lengths of A B and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A C with your eye. Take heed: Data Sufficiency figures are not necessarily 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 drawn to scale. So analyze these problems using your knowledge of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mathematics, not your eye! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: Consider statement (1) alone. Given Rule A (see step 1) to answer 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the question, you need to know whether angle y is congruent to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle’s unidentified angle—the interior angle at point C. Let’s call this 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 angle a. If a 5 y, then the answer to the question is yes. O therwise, the 2 2 12345678901234567890123456789012123456789012345678901 answer is no. In either case, we need to know whether a 5 y in order to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question. Together, angles a and z form a straight line—the line 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passing through points A and C: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a 1 z 5 180 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 5 180 2 z 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The sum of x , y, and a is 180 (Rule C). You can substitute (180 - z) for a in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this equation, and manipulate the result so that it is identical to the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 equation in statement (1): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Rule C (sum of angle measures is 2 x 1 y 1 a 5 180 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 180°) substituting (180 2 z) for a 2 x 1 y 1 ~180 2 z! 5180 2 12345678901234567890123456789012123456789012345678901 subtract 180 from each side add z 2 12345678901234567890123456789012123456789012345678901 x 1y2z50 2 12345678901234567890123456789012123456789012345678901 to each side 2 12345678901234567890123456789012123456789012345678901 x 1 y 5 z 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 172 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 5: Data Sufficiency

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Statement (1) essentially restates a rule that is true for any triangle, so it is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 insufficient alone to answer the question. Eliminate answer choices (A) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and (D) as viable choices. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You could have shortcut this entire analysis had you already been aware 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the rule that an exterior angle of a triangle is always congruent to the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 sum of the two remote interior angles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Step 4: N ow consider statement (2) disregarding statement (1) for now. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The expression (180 2 z) equals our third unidentified angle, which we 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 called a in step 3. Given that (180 2 z) also equals y, the two angles a and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 y are congruent (equal in degree measure). The two sides opposite a and y 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must also be congruent (see Rule A). Thus, statement (2) alone suffices to 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 5: Because statement (1) alone is insufficient to answer the question, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 while statement (2) alone is sufficient, the correct answer choice is (B). 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 There’s no need to consider the two statements together. Based on 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 statement (2), the answer to the question itself is yes, but you don’t need to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 go this far. H ad neither (1) nor (2) alone been sufficient to answer the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 question, you would have then considered both statements together to 2 12345678901234567890123456789012123456789012345678901 2 determine whether the correct answer choice is (C) or (E). 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Success Keys for GMAT Data Sufficiency 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are some basic tips you should follow for Data Sufficiency questions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Apply these keys to Part III’s practice tests, and then review them again 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just before exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Memorize the Answer Choices 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t just learn the directions—memorize the answer choices. (Remem12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ber: they are always the same.) This way you’ll save time because you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t need to refer to them for every question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Be Sure to Consider Each Statement Alone 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 After analyzing statement (1), you’ll be surprised how difficult it can be to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 purge the information in Statement (1) from your mind and start with a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clean slate in considering Statement (2). Be alert at all times to this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 potential problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 173

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Do More Work Than Necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind that the Data Sufficiency format does not require you to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question. So once you’ve convinced yourself that a statement (1 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 or 2) suffices to answer the question, stop right there! You’d only be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wasting your precious time by figuring out the answer itself. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nce you recognized that each statement provides the missing piece to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 compute Judith’s ring cost, you know the correct answer is D. There’s no 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to do the math. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for a Quicker, More Intuitive Route to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Correct Answer 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GM AT is testing, among other skills, your ability to find ingenious, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unconventional, and intuitive solutions to conventional problems. Always 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 look for a shortcut to performing calculations. You’ll save time, and you’ll 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 avoid common computational errors. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you tackle more questions like question 3, you’ll learn to recognize 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 when an answer depends on which values are used, and you won’t have to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bother plugging in “ test” numbers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Perform Endless Calculations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You shouldn’t have to do involved calculations to get to the answer in a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency question. A few simple calculations may be required; but 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 if you’re doing a lot of number crunching, you’ve probably missed the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 mathematical principal the question is asking about. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ad we not used an organized approach to the problem, we would have 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 had no choice but to start plugging in digit after digit (0 through 9). The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more number crunching, the greater the chance for error. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Never Rely Solely on a Diagram (Figure) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Although a figure will conform to the information in the question, it won’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily conform to either statement (1) or (2). So don’t use a Data 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sufficiency figure to estimate or measure values, shapes, lengths, or other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sizes. For example, don’t rely on a figure’s appearance to determine whether: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O ne line segment is longer than another. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O ne angle is larger (greater in degree measure) than another. 2 1 2 174 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Two lines are parallel or perpendicular. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Two triangles are the same shape or size. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O ne segment of a pie chart is larger than another segment. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Rely instead on the numbers and textual information provided in 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the question and statements. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 4 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 In the figure, it appears that A B is equal in length to A C. If you had relied 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the figure, your response to the question would have been wrong! 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Consider All the Possibilities When It Comes to 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Unknowns 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When analyzing a Data Sufficiency question involving unknowns (vari12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ables such as x and y), unless the question explicitly restricts their value, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 consider positive and negative values, as well as fractions and the numbers 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 zero (0) and 1. If the answer to the question depends on what kind of value 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you plug in, then the correct answer must be E. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 We needed to consider negative as well as positive numbers; otherwise, we 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 would have gotten the question wrong. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for Two Statements That Say Essentially the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Same Thing 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Check to see if the two statements provide essentially the same 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information—just in a slightly different form. If they’re the same, you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know the correct answer choice must be either D or E. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that the two statements provided the same information—just in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 different forms 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Check each statement to see if it provides 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers needed to answer the question 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Use this approach for any Data Sufficiency problem involving formulas 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and calculations, where the question asks for a number. In a problem 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 involving rate of motion (speed), for instance, if the question asks for a 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 175

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 speed but does not provide the time (or does not provide the distance), rule 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 out a statement that doesn’t supply the missing piece of the formula. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In analyzing this question, we recognized early that neither statement 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 alone supplies the numbers we need. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Don’t Try to Do All the Work in Your Head 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As with Problem Solving questions, don’t try to do too much work in your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 head. Avoid careless errors by using your pencil and scratch paper for all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 but the simplest mathematical steps. (Remember: Scratch paper and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pencils will be provided at the testing center.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ow far would you get with Q uestion 3 without doing some pencil 2 2 12345678901234567890123456789012123456789012345678901 work—at a minimum, scratching out the two statements in different 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forms? N ot very far! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If You’re Running out of Time, Make a Reasoned 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Guess by Eliminating Answer Choices 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind that if statement (1) alone is insufficient to answer the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question, you can eliminate choices (A) and (D). O n the other hand, once 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ve determined that one of the statements alone is sufficient, you can 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eliminate choices (C) and (E). At this point, your odds of guessing correctly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are 1 in 3, which is a lot better than 1 in 5 for a compete random guess. So 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 if you’re having trouble analyzing one statement, but are confident that the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other statement is sufficient alone, make a guess and move on to the next 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Questions 1–4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In any of the four example questions, we could have stopped part way 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 through our analysis and taken a reasoned guess. Remember: If you can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 get as far as ruling out one answer choice, you can rule out two. At that 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 point, your odds look pretty good! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 176 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level of GM AT Data Sufficiency, along with GM AT 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Data Analysis. At this point, you’ll: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Apply the success keys you learned earlier in the chapter to more 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 challenging Data Sufficiency questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Learn additional success keys that apply to certain types of Data 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sufficiency questions, and apply these keys to example questions 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn a step-by-step approach to handling any Data Analysis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Learn success keys for tackling Data Analysis questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll further explore some of the strategies listed 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above—applying them to GM AT-style questions that are a bit more 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 challenging. You’ll also learn some additional strategies that apply to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain types of Data Sufficiency questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, you’ll take a look at a special type of GM AT Q uantitative problem, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 which the test-makers call D ata A nalysis. These questions involve reading, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 interpreting, and analyzing data presented in graphical form—graphs, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 charts, and tables—and often come in pairs. (Data Analysis questions can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appear in either format—Problem Solving or Data Sufficiency.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency Strategies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this section, you’ll learn strategies for handling Data Sufficiency 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems and see examples of each strategy. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 177

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Plug in “Easy” Numbers—But Don’t Forget 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Negatives, Fractions, Zero, and One 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a Data Sufficiency question involves variables, you can easily confuse 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself by thinking about the problem purely abstractly. You should also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 experiment with different numerical values. Take pencil to paper and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 scratch out some scenarios. This technique will help you see what’s behind 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the problem at hand. Just be sure to try all the different “ types” of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbers that the problem allows (greater numbers, lesser numbers, 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 positive and negative numbers, non-integers, as well as 0 and 1). If the 2 2 12345678901234567890123456789012123456789012345678901 answer to the question depends on what kind of values you plug in, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the correct answer choice must be (E). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a c 2 12345678901234567890123456789012123456789012345678901 If a, b, c, and d are all positive integers, is greater than ? 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 b d 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) a . c 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) b . d 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. N either statement alone allows you to compare 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the values of the two fractions. To see this, try plugging in some simple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers. For example, let a 5 4 and c 5 2, in accordance with statement 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1). Since you can choose any values for b and d, the possible values of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 either fraction are infinite in number, and so you can see that statement (1) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alone is insufficient to answer the question. By the same reasoning, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 statement (2) alone is also insufficient. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, consider the two statements together. Again, let a 5 4 and c 5 2, in 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 accordance with statement (1). N ow, start plugging in some values for b 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and d that meet the condition in statement (2), which is that b . d. Can 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you answer yes to the question? Easily; for example, b 5 1 and d 5 21. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Can you answer no to the question? Easily; here’s just one possible way: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 b 5 4 and d 5 1. Stop here! You’ve found two different answers to the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question and so you know the correct answer must be E. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for Two Statements That Say Essentially the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Same Thing 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In most Data Sufficiency questions, one numbered statement will 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 obviously provide different information than the other statement. But, this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 isn’t always the case. O ne skill that the test-makers will test is your ability 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to recognize two statements that provide essentially the same information— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just in a slightly different form. If they’re the same, you know the correct 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 answer choice must be either (D) or (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 178 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x° 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 C B 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Is the triangle in the figure above equilateral? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) M inor arc A B has a degree measure of 120°. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) x 5 60 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is E. The two statements tell us the same 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 thing—that angle C measures 60°, as it would if the triangle were 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equilateral. But without further information, we can’t tell that angles A 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and B are also 60° angles. It’s possible, for instance, that angle A measures 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 59° while angle B measures 61°—in which case the triangle is not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equilateral. Since we can’t know for sure, the answer must be choice (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The triangle inscribed in the circle certainly look s equilateral (which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 means that all three sides are equal in length). But, the apparent 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 dimensions of the triangle in the diagram are irrelevant to answering the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. O nly the facts given in the question and in the two numbered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statements are important. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Focus on Quantitative Concepts, Not on Number 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Crunching 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Data Sufficiency focuses more on mathematical concepts than on working 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 toward a quantitative solution (which is what Problem Solving questions 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are primarily about). So, be sure to size up the problem at hand. Ask 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 yourself: “ What rule, principle, formula, is the question covering?” O nce 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you’ve figured this out, you should be able to you handle the problem 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without breaking a sweat. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What is the value of p 2 2 q 2 ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) p 1 q 5 24 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (2) p 2 q 5 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 179

Take It to the Next Level

Alert!

Chapter 5: Data Sufficiency

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. M any test-takers would jump headlong into 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trying various values for p and q in trial-and-error fashion. That’s not the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way to approach this problem—or for that matter, any Data Sufficiency 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 problem. Before you evaluate either statement alone, look at the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 expressions given in the problem. Did you notice that p 2 q is the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difference of two squares, and that the expressions given in the two 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 12345678901234567890123456789012123456789012345678901 statements provide its two binomial factors? In other words: p 2 q 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (p 1 q)(p 2 q). This is the concept that the question is designed to cover. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 O nce you see this, handling the problem is a snap. Although neither 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement alone suffices to answer the question (because you’re dealing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with a quadratic rather than a linear equation), statements (1) and (2) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 together provide the two binomials, allowing you to answer the question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (To calculate the answer, you would simply multiply: 24 3 4 5 216.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t do More Work Than Necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind that the Data Sufficiency format does not require you to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question. So once you’ve convinced yourself that a statement (1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or 2) suffices to answer the question, stop right there! You’d only be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wasting your precious time by figuring out the answer itself. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What is the average weight of the 5 members of a football team? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) The average weight of the three heaviest team members is 340 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pounds. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) The two lightest team members weigh 275 and 290 pounds, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respectively. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. To calculate the average of a group of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers, you must have two pieces of information: The total of the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers and the number of numbers. In this case, the only missing piece of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information is the total weight of the team members. (You already know 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the number of numbers involved: 5.) N either statement (1) nor (2) alone 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 gives you the players’ total weight. But if you combine statements (1) and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2), you can determine it. You’d multiply 340 by 3 (to get the combined 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 weight of the heaviest team members) and add 275 and 290 (the weights of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two lightest members). But there’s no need to actually perform these 2 2 12345678901234567890123456789012123456789012345678901 steps. All that matters is that you can tell that it would be theoretically 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible to make these calculations and so determine the average. This is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enough to get the correct answer, choice (C). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 180 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Assume Any Information Not Stated in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Problem 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O ne of the skills the test-makers are measuring is your ability to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinguish facts provided in a Data Sufficiency problem from unsup2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ported assumptions made out of carelessness or inattention. There’s a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 natural tendency to “ invent” facts that aren’t really there so that you can 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer the question. N o test-taker is immune to this tendency. You might 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 be surprised how many “ smart” GM AT test-takers slip up in this way, 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 robbing themselves of precious Q uantitative score points. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What percentage of the female students in a certain history class are 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 majoring in economics? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) 50 percent of the students in the class are male and 50 percent 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 are female. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (2) 50 percent of all students in the class are majoring in economics. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. M any test-takers would carelessly assum e that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the percent of students majoring in economics is the same for the class’s 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 male students as for it’s female students. If this were the case, then you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 could easily answer the question. (The answer would be 50.) But the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 problem provides no information to support this assumption! Thus, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct answer must be choice (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Beware of Statements That Are Irrelevant or That 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Provide Facts Already Supplied in the Question 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Ask yourself what kind of information each statement provides. A state- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment is more likely to be sufficient to answer the question if: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • It provides specific numerical values not given in the premise. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • It adds something new to the premise. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • It provides information that strikes you as relevant to the question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O n the other hand, a statement is more likely to be insufficient to answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the question if: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 • It does not provide any specific numerical values that the premise 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 leaves unknown. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • It seems redundant—simply paraphrasing the premise (or some 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 part of it). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The information strikes you as irrelevant to the premise or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 181

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A certain granola recipe calls for a simple mixture of raisins costing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $3.50 per pound with oats. At a cost of $2.00 per pound for the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 granola mixture, how many pounds of oats must be added to 10 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 pounds of raisins? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) The granola mixture is packaged in one-pound bags. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (2) O ats cost $1.00 per pound. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is A. The question itself provides two of the three 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 facts you need to answer it: the cost per pound of raisins and the cost per 2 2 12345678901234567890123456789012123456789012345678901 pound of the mixture. Statement (1) alone provides no useful information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for answering the question. So, without even looking at statement (1), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ve eliminated answer choices (A), (C), and (D)! Statement (2) provides 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the third needed fact: the cost per pound of oats. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although you don’t need to do the math, here’s how you would answer the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question with the additional information provided by statement (2). Think 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the quantities as costs per pound and multiply the cost by the weight. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The total mixture will consist of 10 pounds of raisins at $3.50 per pound, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or ($3.50)(10), plus “ x ” pound of oats at $1.00 per pound, or ($1.00)(x ). 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The mixture costs $2.00 per pound, and it will be (10 1 x ) pounds: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~3.50!~10! 1 ~1.00!~x ! 5 ~2.00!~10 1 x ! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 35 1 x 5 20 1 2x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 15 5 x 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 15 pound of oats are needed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Assume That Any Diagrams Provided Are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Accurate 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although a diagram will conform to the information in the question, it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 won’t necessarily conform to either statement (1) or (2). So don’t use a 2 2 12345678901234567890123456789012123456789012345678901 Data Sufficiency figure to estimate or measure values, shapes, lengths, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other sizes. For example, don’t rely on a figure’s appearance to determine: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Whether one line segment is longer than another 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Whether one angle is larger (greater in degree measure) than another 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Whether two lines are parallel or perpendicular 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Whether two triangles are the same shape or size 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Whether one segment of a pie chart is larger than another segment 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Rely instead on the numbers and the textual information provided 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the question and in the two statements. 2 12345678901234567890123456789012123456789012345678901 2 1 2 182 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the figure above, is l1 parallel to l2 ? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 (1) q 1 y 5 s 1 w 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2) p 1 x 5 180 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is B. If you were to rely on the appearance of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 figure, you’d see that the two lines look parallel. But, remember: When it 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 comes to GM AT Data Sufficiency, never measure with your eye! Rely 2 12345678901234567890123456789012123456789012345678901 instead on the numbers and other information in the problem. H ere’s how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to analyze this problem. Vertical angles (formed by intersecting lines) are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 always congruent. Thus, q 5 s and y 5 w . Accordingly, q 1 y must equal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 s 1 w in any event, and statement (1) alone does not suffice to answer the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. Given statement (2) alone, since p and x are supplementary, p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 must equal y as well as w (because y 1 x 5 180 and w 1 x 5 180). Thus, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corresponding angles are congruent and the two lines are parallel. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Analysis Strategies 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Data Analysis questions are designed to gauge your ability to read and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 analyze data presented in statistical charts, graphs, and tables—and to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 calculate figures such as percentages, ratios, fractions, and averages based 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 on the numbers you glean from graphical data. Data Analysis questions 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can appear in either of the two basic formats: Problem Solving and Data 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Sufficiency. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Expect to find 2–4 Data Analysis questions (typically in sets of two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questions) interspersed with other Q uantitative questions. Each question 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in a set pertains to the same graphical data. Each question (and each set) 2 12345678901234567890123456789012123456789012345678901 22 involves either one or tw o distinct graphical displays. Four types appear 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most frequently: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Pie charts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Tables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Bar graphs 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 4. Line graphs 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 183

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Data Analysis—Your 5-Step Game Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 There are 5 basic steps for handling a GM AT Data Analysis question—or 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set of questions. In this section, you’ll learn these steps, and then apply 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 them to the following two sample questions, both based on the same two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pie charts. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1. INCOME AND EXPENSES–DIVISIONS A, B, C, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 AND D OF XYZ COMPANY (YEAR X) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 During year X, by approximately what amount did Division C’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 income exceed Division B’s expenses? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. $125,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $127,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. $140,000 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. $180,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $312,000 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. With respect to the division whose income exceeded its expenses by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the greatest percent among the four divisions, by approximately 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 what amount did the division’s income exceed its own expenses? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. $69,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $90,000 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. $150,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. $185,000 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. $230,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 184 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 5: Data Sufficiency

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Before learning and applying the 5 steps, note the following key features of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Analysis question sets: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The questions tend to be long and wordy. Get used to it; that’s the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way the test-makers design them. You’ll probably find that you have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more trouble interpreting the questions than the figures. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Bar graphs and line charts are drawn to scale. (You’ll see a bar graph 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and a line chart during this chapter’s M ini-Test.) Pie charts will are 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 not necessarily drawn to scale (you’ll see a note letting you know that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 it’s not). Visual scale is irrelevant when it comes to analyzing tables. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Important assumptions will be provided. Any additional informa2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 tion that you might need to know to interpret the figures will be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indicated above and below the figures. (Be sure to read this 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • N early all questions ask for an approximation. You’ll see some form 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the word approx im ate in nearly all Data Analysis questions. This 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is because the test-makers are trying to gauge your ability to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 interpret graphical date, not your ability to crunch numbers to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ nth” decimal place. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M any of the numbers used are alm ost round. This feature relates to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the previous one. The GM AT rewards test-takers who recognize 2 2 12345678901234567890123456789012123456789012345678901 that rounding off numbers (to an appropriate extent) will suffice to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 get to the right answer. So they pack Data Analysis figures with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers that are close to “ easy” ones. (The numbers in our pie 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 chart set serve as good examples. For example, $1,560,000 is close 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to $1,500,000 million and $495,000 is close to $500,000.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Figures are not drawn to deceive you or to test your eyesight. In bar 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 graphs and line charts, you won’t be asked to split hairs to determine 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 values. These figures are designed with a comfortable margin for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 error in visual acuity. Just don’t round up or down too far. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The 5-Step Plan 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere’s the 5-step approach that will help you to handle any set of Data 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analysis questions. Just a few pages ahead, we’ll apply this approach to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 this 2-question set on page 187. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 1: Look at the “ big picture” first. Before plunging into the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question(s), read all the information above and below the figure(s). Look 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 particularly for: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Totals (dollar figures or other numbers) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Whether the numbers are in thousand or millions 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 185

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • H ow two or more figures are labeled 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Whether graphical data is expressed in numbers or percentages 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Read the entire Data Analysis question very carefully. As you do, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 divide the question into parts, each of which involves a distinct step in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 getting to the answer. Pay particular attention to whether the question 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 asks for: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • An approximation 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • A percentage or a raw number 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A comparison 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • An increase or a decrease 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In breaking the question down into tasks, look for a shortcut to save 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 yourself work. (M any Data Analysis questions can be answered either the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 quick way or the slow way.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: Perform the steps needed to get to the answer. Look for a shortcut 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the answer. Round numbers up or down (but not too far) as you go. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Check choices (A) through (E) for your answer. If the question 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 asks for a number, find the choice closest to your answer. Look for other 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices are “ too close for comfort.” If you see any, or if your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution is nowhere near any of the choices, go to Step 5. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5: Check your calculations, and make sure the value and form 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (number, percentage, total, etc.) of your solution conforms with what the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question asks. Check your rounding technique. Did you round off in the 2 2 12345678901234567890123456789012123456789012345678901 wrong direction? Did you round off too far? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Apply the 5-Step Plan 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It’s time to go back to the sample question set you looked at a few pages 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 back. Let’s walk through both questions, using the 5-step game plan you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just learned. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: Size up the two charts, and read the information above and below 2 2 12345678901234567890123456789012123456789012345678901 them. N otice that we’re only dealing with one company during one year 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here. N otice also that dollar totals are provided, but that the pie segments 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are expressed only as percentages. That’s a clue that your main task in this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set will be to calculate dollar amounts for various pie segments. N ow read 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the first question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Question 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Q uestion 1 is a moderately difficult question. Approximately 50% of 2 2 12345678901234567890123456789012123456789012345678901 1 test-takers respond correctly to questions like it. H ere’s the question again: 2 2 186 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. During year X, by approximately what amount did Division C’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 income exceed Division B’s expenses? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. $125,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $127,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. $140,000 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 D. $180,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $312,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 You already performed step 1, so move ahead to step 2. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: This question involves three tasks: (1) calculate Division C’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 income, (2) calculate Division B’s expenses, and (3) compute their 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difference. There’s no shortcut to these three tasks, so go on to step 3. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: Division B’s expenses accounted for 26% of XYZ ’s total 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 expenses, given as $495,000. Rounding off these figures to 25% and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 $500,000, Division B’s expenses totaled approximately $125,000. Income 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from Division C sales was 20% of total XYZ income, given as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $1,560,000. Rounding this total down to $1,500,000, income from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Division C sales was approximately $300,000. Income from Division C 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sales exceeded Division B’s expenses by approximately $175,000. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 4: The only answer choice close to this solution is (D). If you have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 extra time, go to step 5. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 5: M ake sure you started with the right numbers. Did you compare 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 C’s income with B’s expense (and not some other combination)? If you’re 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 satisfied that the numbers you used were the right ones and that your 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 calculations are okay, move on to the next question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Question 2 2 12345678901234567890123456789012123456789012345678901 Q uestion 2 is a difficult question. Approximately 30% of test-takers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond correctly to questions like it. H ere’s the question again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. With respect to the division whose income exceeded its own 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expenses by the greatest percent among the four divisions, by 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 approximately what amount did the division’s income exceed its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 own expenses? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. $69,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $90,000 2 12345678901234567890123456789012123456789012345678901 C. $150,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. $185,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $230,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 187

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 2: This is a complex question. First, you need to compare 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 profitability—in dollar amount—among the four divisions. You can rule 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 out Division B, since its expenses exceeded its income. That leaves 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 Divisions A, C, and D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: For Divisions A, C, and D, compare percent of income and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 percent of expenses: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Division A: 38% of total income and 35% of total expenses 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 (37% difference) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Division C: 20% of total income and 14% of total expenses 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (6% difference) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Division D: 30% of total income and 26% of total expenses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (4% difference) 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Division C’s income was a bit more than $300,000 (20% of $1,500,000). 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Division C’s expenses were approximately $75,000 (15% of $500,000). 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Division C’s income exceeded it’s expenses by approximately $225,000. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Answer choice (E), $230,000, is the only one close to our 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 approximation. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 5: If you have time, rethink Step 3. M ake sure you’re convinced that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Division C’s percentage profit was greater than either A’s or D’s. Also, ask 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself if $230,000 in the right ballpark. If you’re confident in your 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 analysis, move on to the next question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for GMAT Data Analysis 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere are some basic tips you should follow for any type of Data Analysis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. Apply these keys to Part III’s practice tests, and then review them 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 again just before exam day. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Scroll Vertically to See the Entire Display 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Some vertical scrolling may be necessary to view the entire display, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 especially the information above and below the chart, graph, or table. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t forget to scroll up and down as you analyze each question. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Confuse Percentages with Raw Numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ost data analysis questions involve raw data as well as proportion—in 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms of either percent, fraction, or ratio (usually percent). Always ask 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself: “ Is the solution to this problem a raw number or a proportional 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number?” You can be sure that the testing service will “ bait” you with 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appealing incorrect answer choices! 2 12345678901234567890123456789012123456789012345678901 2 1 2 188 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 5: Data Sufficiency

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Be Sure to Go to the Appropriate Chart (Or Part of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A Chart) for Your Numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This point of advice may seem obvious; nevertheless, reading the wrong 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 data is probably the leading cause of incorrect responses to data analysis 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions! To ensure that you don’t commit this careless error, point your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 finger to the proper line, column, or bar on the screen; put your finger right 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 on it, and don’t move it until you’re sure you’ve got the correct data. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 To Save Time, Round Off Numbers—But Don’t Distort Values 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ost Data Analysis questions ask for approximate values. So, to save time, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it’s okay to round off numbers; rounding off to the nearest appropriate unit 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 or half-unit usually suffices to get to the correct answer. But don’t get too 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rough in your approximations. Also, be sure to round off numerators and 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 denominators of fractions in the same direction (either both up or both 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 down), unless you’re confident that a rougher approximation will suffice. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O therwise, you’ll distort the value of the number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Handle Lengthy, Confusing Questions One Part at a Time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Data Analysis questions can be wordy and confusing. Don’t panic. Keep in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 mind that lengthy questions almost always call for two discreet tasks. For 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the first task, read only the first part of the question. When you’re done, go 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 back to the question and read the next part. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Split Hairs in Reading Line Charts and Bar Graphs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These are the two types of figures that are drawn to scale. If a certain point 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 on a chart appears to be about 40% of the way from one hash mark to the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 next, don’t hesitate to round up to the halfway point. (The number 5 is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 usually easier to work with than 4 or 6.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Formulate a Clear Idea as to the Overall Size of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Number the Question is Calling for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The test-makers pack Data Analysis questions with “ sucker bait” answer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices for test-makers who make common computational errors. The 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 best way to keep yourself from falling into their trap is to ask yourself 2 12345678901234567890123456789012123456789012345678901 what sort of ballpark number you’re looking for in a correct answer. You 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might ask yourself: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Is it a double digit number? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Is it a percentage that is obviously greater than 50 percent? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Is it a great raw number in the thousands? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 By keeping the big picture in mind, you’ll catch the fact that you made an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 error in calculation. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 189

Chapter

6 Math Review—Number Forms, Relationships, and Sets 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this chapter, first you’ll focus on various forms of numbers and 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relationships between numbers. Specifically, you’ll learn how to: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Combine fractions using the four basic operations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Combine decimal numbers by multiplication and division 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Compare numbers in percentage terms 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Compare percent changes with number changes 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Rewrite percents, fractions, and decimal numbers written in one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 form as another 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Determine ratios between quantities and determine quantities from 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ratios 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Set up equivalent ratios (proportions) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext, you’ll explore the following topics, all of which involve sets (defined 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 groups) of numbers or other objects: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Simple average and median (two ways that a set of numbers can be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 described as a whole) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Arithmetic series (the pattern from one number to the next in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 linear sequence of numbers) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Permutations (the possibilities for arranging a set of objects) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Combinations (the possibilities for selecting groups of objects from 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a set) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Probability (the statistical chances of a certain event, permutation, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or combination occurring) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 190

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Alert!

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although this is the most basic of all the math-review chapters in this 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 book, don’t think for a minute that you should skip it. The skills covered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here are basic building blocks for other types of questions—the ones 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll encounter in the chapters to follow. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Percent, Fraction, and Decimal Equivalences 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Any real number can be expressed as a fraction, a percent, or a decimal 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number. For instance, , 20% , and .2 are all different forms of the same 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 10 1 2 12345678901234567890123456789012123456789012345678901 quantity, or value. GM AT math questions often require you to rewrite one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 form as another as part of solving the problem at hand. You should know 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 how to write any equivalence quickly and confidently. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To rewrite a percent-as-a-decimal, move the decimal point two places to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the left (and drop the percent sign). To rewrite a decimal-as-a-percent, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 move the decimal point two places to the right (and add the percent sign). 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9.5% 5 .095 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .004 5 .4% 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To rewrite a percent-as-a-fraction, divide by 100 (and drop the percent 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sign). To rewrite a fraction-as-a-percent, m ultiply by 100 (and add the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent sign). Percents greater than 100 are equivalent to numbers greater 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 than 1. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 810 81 1 2 12345678901234567890123456789012123456789012345678901 810% 5 5 58 2 12345678901234567890123456789012123456789012345678901 100 10 10 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 75 1 3 300 2 12345678901234567890123456789012123456789012345678901 5 % 5 % 5 37 % 2 12345678901234567890123456789012123456789012345678901 8 8 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Percents greater than 100 or less than 1 (such as 457% and .067% ) can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be confusing, because it’s a bit harder to grasp the magnitude of these 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers. To guard against errors when writing, keep in mind the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 general magnitude of the number you’re dealing with. For example, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 think of .09% as just less than .1% , which is one-tenth of a percent, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .4 2 12345678901234567890123456789012123456789012345678901 a thousandth (a pretty small valued number). Think of as just less 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 .5 1 2 12345678901234567890123456789012123456789012345678901 than , which is obviously , or 10% . Think of 668% as more than 6 2 12345678901234567890123456789012123456789012345678901 5 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 times a complete 100% , or between 6 and 7. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 191

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To rewrite a fraction as a decimal, simply divide the numerator by the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 denominator, using long division. A fraction-to-decimal equivalence might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 result in a precise value, an approximation with a repeating pattern, or an 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 approximation with no repeating pattern: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The equivalent decimal number is precise after three 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 .625 decimal places. 2 12345678901234567890123456789012123456789012345678901 8 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The equivalent decimal number can only be approxi5 2 12345678901234567890123456789012123456789012345678901 ' .555 2 12345678901234567890123456789012123456789012345678901 mated (the digit 5 repeats indefinitely). 2 12345678901234567890123456789012123456789012345678901 9 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The equivalent decimal number can only be approxi5 2 12345678901234567890123456789012123456789012345678901 '.714 2 12345678901234567890123456789012123456789012345678901 mated (there is no repeating pattern by carrying the 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 calculation to additional decimal places). 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Certain fraction-decimal-percent equivalents show up on the GM AT more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 often than others. The numbers in the following tables are the test-makers’ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 favorites because they reward test-takers who recognize quick ways to deal 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with numbers. M emorize these conversions so that they’re second nature 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to you on exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Percent Decimal Fraction 2 Percent Decimal Fraction 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 1 1 2 12345678901234567890123456789012123456789012345678901 50% .5 16 % .16 2 12345678901234567890123456789012123456789012345678901 3 3 6 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 5 1 1 2 12345678901234567890123456789012123456789012345678901 % .83 83 25% .25 2 12345678901234567890123456789012123456789012345678901 3 3 6 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 1 75% .75 20% .2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 40% .4 1 2 12345678901234567890123456789012123456789012345678901 10% .1 5 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 60% .6 3 2 12345678901234567890123456789012123456789012345678901 30% .3 5 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 80% .8 7 2 12345678901234567890123456789012123456789012345678901 5 70% .7 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 .125 9 12 % 2 12345678901234567890123456789012123456789012345678901 90% .9 2 8 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 3 1 2 12345678901234567890123456789012123456789012345678901 .375 37 % 2 12345678901234567890123456789012123456789012345678901 1 1 1 2 8 2 12345678901234567890123456789012123456789012345678901 % .33 33 2 12345678901234567890123456789012123456789012345678901 1 5 3 3 3 2 12345678901234567890123456789012123456789012345678901 .625 62 % 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .66 66 % 1 7 2 12345678901234567890123456789012123456789012345678901 3 3 3 .875 87 % 2 12345678901234567890123456789012123456789012345678901 2 1 2 8 2 192 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Simplifiying and Combining Fractions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to combine fractions using one or more 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the four basic operations (addition, subtraction, multiplication, and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 division). The rules for combining fractions by addition and subtraction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are very different than the ones for multiplication and division. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Addition and Subtraction and the LCD 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 To combine fractions by addition or subtraction, the fractions m ust have a 2 2 12345678901234567890123456789012123456789012345678901 common denominator. If they already do, simply add (or subtract) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numerators. If they don’t, you’ll need to find one. You can always multiply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 all of the denominators together to find a common denominator, but it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might be a big number that’s clumsy to work with. So instead, try to find 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the least (or low est) com m on denom inator (LCD) by working your way up 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in multiples of the largest of the denominators given. For denominators of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6, 3 and 5, for instance, try out successive multiples of 6 (10, 12, 18, 24 . . . 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ), and you’ll hit the LCD when you get to 30. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5 5 2 12345678901234567890123456789012123456789012345678901 2 1 5 2 12345678901234567890123456789012123456789012345678901 3 6 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 15 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 11 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 15 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 15 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. To find the LCD, try out successive multiples 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of 6 until you come across one that is also a multiple of both 3 and 2. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 LCD is 6. M ultiply each numerator by the same number by which you 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 would multiply the fraction’s denominator to give you the LCD of 6. Place 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the three products over this common denominator. Then, combine the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numbers in the numerator. (Pay close attention to the subtraction sign!) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Finally, simplify to lowest terms: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 193

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 1 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5 5 5~10! 2 5~5! 1 5~15! 2 12345678901234567890123456789012123456789012345678901 2 1 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 6 2 30 2345678901234567890123456789012123456789012345678901 2 1 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 5 15 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 50 2 25 1 75 2345678901234567890123456789012123456789012345678901 2 1 5 2 12345678901234567890123456789012123456789012345678901 30 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 10 100 2 12345678901234567890123456789012123456789012345678901 , or 5 2 12345678901234567890123456789012123456789012345678901 30 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Multiplication and Division 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To multiply fractions, multiply the numerators and multiply the denomi- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nators. The denominators need not be the same. To divide one fraction by 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another, multiply by the reciprocal of the divisor (the number after the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 division sign). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D ivision: M ultiplication: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 1 ~1!~1!~1! 1 1 2 12345678901234567890123456789012123456789012345678901 3 3 5 5 5 2 4 (2)(4) 8 2 12345678901234567890123456789012123456789012345678901 5 5 3 5 2 3 7 ~2!~3!~7! 42 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 4 3 (5)(3) 15 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To simplify the multiplication or division, cancel factors common to a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numerator and a denominator before combining fractions. It’s okay to 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 4 3 2 12345678901234567890123456789012123456789012345678901 cancel across fractions. Take, for instance the operation 3 3 . 2 12345678901234567890123456789012123456789012345678901 4 9 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Looking just at the first two fractions, you can factor out 4 and 3, so the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 3 12345678901234567890123456789012123456789012345678901 operation simplifies to 3 3 . N ow, looking just at the second and 2 2 12345678901234567890123456789012123456789012345678901 1 3 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 third fractions, you can factor out 3 and the operation becomes even 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 1 1 2 12345678901234567890123456789012123456789012345678901 3 3 5 . simpler: 2 12345678901234567890123456789012123456789012345678901 1 1 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Apply the same rules in the same way to variables (letters) as to numbers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 194 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 b a 8 2 2 12345678901234567890123456789012123456789012345678901 3 3 3 5? 2 12345678901234567890123456789012123456789012345678901 a 4 5 c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ab 2 12345678901234567890123456789012123456789012345678901 A. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10b 2 12345678901234567890123456789012123456789012345678901 B. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 9c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 C. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 16b 2 12345678901234567890123456789012123456789012345678901 D. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 5ac 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4b 2 12345678901234567890123456789012123456789012345678901 E. 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5c 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is E. Since you’re dealing only with multiplication, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 look for factors and variables (letters) in any numerator that are the same 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as those in any denominator. Canceling common factors leaves 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 b 1 2 2 12345678901234567890123456789012123456789012345678901 3 3 3 . 2 12345678901234567890123456789012123456789012345678901 1 1 5 c 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4b 2 12345678901234567890123456789012123456789012345678901 M ultiply numerators and combine denominators and you get . 2 12345678901234567890123456789012123456789012345678901 5c 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Mixed Numbers and Multiple Operations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A m ix ed num ber consists of a whole number along with a simple 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 fraction—for example, the number 4 . Before combining fractions, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 might need to rewrite a mixed number as a fraction. To do so, follow these 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 three steps: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. M ultiply the denominator of the fraction by the whole number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Add the product to the numerator of the fraction. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Place the sum over the denominator of the fraction. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 For example, here’s how to rewrite the mixed number 4 into a fraction: 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 ~3!~4! 1 2 14 2 12345678901234567890123456789012123456789012345678901 5 4 5 2 12345678901234567890123456789012123456789012345678901 3 3 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To perform multiple operations, always perform multiplication and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 division before you perform addition and subtraction. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 195

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 23 5? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 3 2345678901234567890123456789012123456789012345678901 2 1 1 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 1 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 11 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 17 D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 11 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is (A). First, rewrite all mixed numbers as fractions. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, eliminate the complex fraction by multiplying the numerator 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fraction by the reciprocal of the denominator fraction (cancel across 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fractions before multiplying): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 9 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 11 9 8 1 4 11 11 4 11 2 12345678901234567890123456789012123456789012345678901 5 5 5 2 2 2 2 2 12345678901234567890123456789012123456789012345678901 3 2 9 3 1 1 3 1 3 9 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, express each fraction using the common denominator 3, then 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 subtract: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 11 12 2 11 1 2 12345678901234567890123456789012123456789012345678901 2 5 5 2 12345678901234567890123456789012123456789012345678901 1 3 3 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Place Value and Operations with Decimals 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Place value refers to the specific value of a digit in a decimal. For example, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 in the decimal 682.793: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The digit 6 is in the “ hundreds” place. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The digit 8 is in the “ tens” place. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The digit 2 is in the “ ones” place. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 196 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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S DS D

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The digit 7 is in the “ tenths” place. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The digit 9 is in the “ hundredths” place. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The digit 3 is in the “ thousandths” place. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So, you can express 682.793 as follows: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 9 3 7 2 12345678901234567890123456789012123456789012345678901 1 1 . 600 1 80 12 1 2 12345678901234567890123456789012123456789012345678901 10 100 1,000 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 To approximate, or round off, a decimal, round any digit less than 5 down 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to 0, and round any digit greater than 5 up to 0 (adding one digit to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 place value to the left). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The value of 682.793, to the nearest hundredth, is 682.79. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The value of 682.793, to the nearest tenth, is 682.8. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The value of 682.793, to the nearest whole number, is 683. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The value of 682.793, to the nearest ten, is 680. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The value of 682.793, to the nearest hundred, is 700. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Multiplying decimals. The number of decimal places (digits to the right 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the decimal point) in a product should be the same as the total number 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of decimal places in the numbers you multiply. So to multiply decimals 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quickly: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. M ultiply, but ignore the decimal points. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Count the total number of decimal places among the numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you multiplied. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Include that number of decimal places in your product. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere are two simple examples: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (23.6)(.07) 3 decimal places altogether 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (236)(7) 5 1652 Decimals temporarily ignored 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (23.6)(.07) 5 1.652 Decimal point inserted 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (.01)(.02)(.03) 6 decimal places altogether 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1)(2)(3) 5 6 Decimals temporarily ignored 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (.01)(.02)(.03) 5 .000006 Decimal point inserted 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 197

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Dividing decimal numbers. When you divide (or compute a fraction), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you can move the decimal point in both numbers by the same number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 places either to the left or right without altering the quotient (value of the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 fraction). H ere are three related examples: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 11.4 114 2345678901234567890123456789012123456789012345678901 2 1 11.4 4 .3 5 5 5 38 2 12345678901234567890123456789012123456789012345678901 .3 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1.14 14 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1.14 4 3 5 5 5 .38 2 12345678901234567890123456789012123456789012345678901 3 300 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 114 11,400 2 12345678901234567890123456789012123456789012345678901 5 5 3,800 114 4 .003 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .003 3 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Eliminate decimal points from fractions, as well as from percents, to help 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you see more clearly the magnitude of the quantity you’re dealing with. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions involving place value and decimals usually require a 2 2 12345678901234567890123456789012123456789012345678901 bit more from you than just identifying a place value or moving around 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a decimal point. Typically, they require you to combine decimals with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fractions or percents. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 Which of the following is nearest in value to 3 .3 3 3 .03? 2 12345678901234567890123456789012123456789012345678901 3 30 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 99 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 1,000,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 33 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 100,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 99 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 100,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 33 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 10,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 99 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is (A). There are several ways to convert and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 combine the four numbers provided in the question. O ne method is to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 1 2 12345678901234567890123456789012123456789012345678901 combine the two fractions: 3 5 . Then, combine the two decimals: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 30 90 2 12345678901234567890123456789012123456789012345678901 .3 3 .03 5 .009. Finally, combine the two products: .011 3 .009 ' 2 1 2 198 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 .000099. Each answer choice expresses a fraction, so you need to rewrite 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .000099 as a fraction by carefully counting place values. The final digit is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the “ millionth” place. Choice (A) provides the fractional equivalent of 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 this number. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Simple Problems Involving Percent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, a simple problem involving percent might ask you to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 perform any one of these four tasks: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Find a percent of a percent. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. Find a percent of a number. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Find a number when a percent is given. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Find what percent one number is of another. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The following examples show you how to handle these four tasks (task 4 is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a bit trickier than the others): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 W hat is 2% of 2% ? 1. Finding a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent of a Rewrite 20% as .20, then multiply: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent 2 12345678901234567890123456789012123456789012345678901 .02 3 .02 5 .004, or .4% 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 W hat is 35% of 65? 2. Finding a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent of a 2 12345678901234567890123456789012123456789012345678901 Rewrite 35% as .35, then multiply: 2 12345678901234567890123456789012123456789012345678901 number 2 12345678901234567890123456789012123456789012345678901 .35 3 65 5 22.75 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 is 14% of w hat num ber? 3. Finding a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number when a 2 12345678901234567890123456789012123456789012345678901 Translate the question into an algebraic 2 12345678901234567890123456789012123456789012345678901 percent is given 2 12345678901234567890123456789012123456789012345678901 equation, writing the percent as either a 2 12345678901234567890123456789012123456789012345678901 fraction or decimal: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 5 14% of x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 5 .14x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 1 100 2 12345678901234567890123456789012123456789012345678901 x5 5 5 5 50 2 12345678901234567890123456789012123456789012345678901 .14 .02 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 199

Part III: Q uantitative A bility

www.petersons.com

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 90 is w hat % of 1,500? 4. Finding what 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent one 2 12345678901234567890123456789012123456789012345678901 Set up an equation to solve for the percent: 2 12345678901234567890123456789012123456789012345678901 number is of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 another 2 12345678901234567890123456789012123456789012345678901 90 x 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 1,500 100 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1,500x 59,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 15x 5 90 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 90 2 12345678901234567890123456789012123456789012345678901 x 5 , or 6 2 12345678901234567890123456789012123456789012345678901 15 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Percent Increase and Decrease 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In example 4, you set up a proportion. (90 is to 1,500 as x is to 100.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll need to set up a proportion for other types of GM AT questions as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 well, including questions about ratios, which you’ll look at a bit later in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this chapter. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The concept of percent change is one of the test-makers’ favorites. H ere’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the key to answering questions involving this concept: Percent change 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 always relates to the value before the change. H ere are two simple 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 illustrations: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 10 increased by 1. The amount of the increase is 2. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w hat percent is 12? 2 12345678901234567890123456789012123456789012345678901 2. Compare the change (2) to the original 2 12345678901234567890123456789012123456789012345678901 number (10). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. The change in percent is , or 20. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12 decreased by 1. The amount of the decrease is 2. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w hat percent is 10? 2 12345678901234567890123456789012123456789012345678901 2. Compare the change (2) to the original 2 12345678901234567890123456789012123456789012345678901 number (12). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3. The change is , or 16 , or approxi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 3 2 12345678901234567890123456789012123456789012345678901 mately 16.6% . (Did you remember from 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the equivalents table on page 192 that?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 200 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N otice that the percent increase from 10 to 12 (20% ) is not the same as the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent decrease from 12 to 10 (16 % ). That’s because the original 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 number (before the change) is different in the two questions. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A typical GM AT percent-change problem will involve a story—about a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 type of quantity such as tax, profit or discount, or weight—in which you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to calculate successive changes in percent. For example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • An increase, then a decrease (or vice versa) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • M ultiple increases or decreases 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Whatever the variation, just take the problem one step at a time and you’ll 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have no trouble handling it. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A stereo system original priced at $500 is discounted by 10% , then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by another 10% . If a 20% tax is added to the purchase price, how 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 much would a customer buying the system at its lowest price pay 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for it, including tax, to the nearest dollar? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. $413 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $480 2 12345678901234567890123456789012123456789012345678901 C. $486 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. $500 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $512 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. After the first 10% discount, the price was 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 $450 ($500 minus 10% of $500). After the second discount, which is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculated based on the $450 price, the price of the stereo is $405 ($450 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 minus 10% of $450). A 20% tax on $405 is $81. Thus, the customer has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paid $405 1 $81 5 $486. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 201

Part III: Q uantitative A bility

Price

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A percent-change problem might also involve an accompanying chart or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 graph, which provides the numbers needed for the calculation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Holden Software 2 12345678901234567890123456789012123456789012345678901 Stock Price 2 12345678901234567890123456789012123456789012345678901 200 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 180 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 160 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 140 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 120 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 100 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 80 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 60 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 40 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 20 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 0 1992 1993 1994 1995 1996 1997 1998 2 12345678901234567890123456789012123456789012345678901 Year 2 12345678901234567890123456789012123456789012345678901 Annual High Annual Low 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Based on the graph above, the average low price of H olden Soft2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ware stock for the two-year period 1993–1994 was approximately 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 what percent lower than its average high price for the two-year 2 12345678901234567890123456789012123456789012345678901 period 1996–1997? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 37 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 45 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 52 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 75 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Average low prices (represented by black bars) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 for 1993 and 1994 were $60 and $80, respectively—which yield an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 average of $70 for the two-year period. Average high prices (represented 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by gray bars) for 1996 and 1997 were approximately $190 and $100, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 respectively—which yield an average of $145. The percent decrease from 2 2 12345678901234567890123456789012123456789012345678901 $145 to $70 is just less than 50% . The only possible answer choice is (C). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 202 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If a question based on a bar graph, line graph, or pie chart asks for an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 approximation, the test-makers are telling you that it’s okay to round off 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 numbers you glean from the chart or graph. For example, in the preceding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question, a rough estimate of $145 for the high 1996 average was close 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enough to determine the correct answer choice. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ratios and Proportion 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 A ratio expresses proportion or comparative size—the size of one quantity 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relative to the size of another. As with fractions, you can simplify ratios to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simplest form by dividing common factors. For example, given a class of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 28 students—12 freshmen and 16 sophomores: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The ratio of freshmen to sophomores is 12:16 , or 3:4. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The ratio of freshmen to the total number of students is 12:28, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or 3:7. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The ratio of sophomores to the total number of students is 16:28, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or 4:7. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Finding a Ratio 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to determine a ratio based on given 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 quantities. This is the easiest type of GM AT ratio question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A class of 56 students contains only freshmen and sophomores. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If 21 of the students are sophomores, what is the ratio between 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the number of freshmen and the number of sophomores in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the class? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 3:5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5:7 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 5:3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 7:4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 2:1 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Since 21 of 56 students are sophomores, 35 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 must be freshman. The ratio of freshmen to sophomores is 35:21. To 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 simplify the ratio to simplest term, divide both numbers by 7, giving you a 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ratio of 5:3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Determining Quantities from a Ratio 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Part-to-Whole Analysis) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can think of any ratio as parts adding up to a whole. For example, in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 the ratio 5:6, 5 parts 1 6 parts 5 11 parts (the whole). If the actual total 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 203

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 quantity were 22, you’d multiply each element by 2: 10 parts 1 12 parts 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 parts (the whole). N otice that the ratios are the same: 5:6 is the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ratio as 10:22. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 You might be able to solve a GM AT ratio question using this part-to2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whole approach. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A class of students contains only freshmen and sophomores. If 18 of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the students are sophomores, and if the ratio between the number 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 of freshmen and the number of sophomores in the class is 5:3, how 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 many students altogether are in the class? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 30 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. 36 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 40 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 48 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 56 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. Using a part-to-whole analysis, look first at the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ratio and the sum of its parts: 5 (freshman) 1 3 (sophomores) 5 8 (total 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 students). These aren’t the actual quantities, but they’re proportionate to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 those quantities. Given 18 sophomores altogether, sophomores account 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for 3 parts—each part containing 6 students. Accordingly, the total 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of students must be 6 3 8 5 48. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Determining Quantities from a Ratio (Setting Up a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Proportion) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Since you can express any ratio as a fraction, you can set two equivalent, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or proportionate, ratios equal to each other, as fractions. So the ratio 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 16 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 5 . If one of the four 2 16:28 is proportionate to the ratio 4:7 because 2 12345678901234567890123456789012123456789012345678901 28 7 2 12345678901234567890123456789012123456789012345678901 terms is missing from the equation (the proportion), you can solve for the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 missing term using algebra. So if the ratio 3:4 is proportionate to 4:x , you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 4 2 12345678901234567890123456789012123456789012345678901 can solve for x in the equation 5 . Using the cross-product method, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 x 2 12345678901234567890123456789012123456789012345678901 equate product of numerator and denominator across the equation: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~3!~x ! 5 ~4!~4! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3x 5 16 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 16 1 2 12345678901234567890123456789012123456789012345678901 x 5 , or 5 2 12345678901234567890123456789012123456789012345678901 3 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 204 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O r, since the numbers are simple, shortcut the algebra by asking yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what number you multiply the first numerator (3) by for a result that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equals the other numerator (4): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 3 3 5 4 (a no-brainer calculation). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 So you maintain proportion (equal ratios) by also multiplying the first 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 denominator (4) by : 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 16 4 2 12345678901234567890123456789012123456789012345678901 5 (another no-brainer calculation) 4 3 2345678901234567890123456789012123456789012345678901 2 1 3 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Even if the quantities in a question strike you as decidedly “ unround,” it’s 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a good bet that doing the math will be easier than you might first think. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If 3 miles is equivalent to 4.83 kilometers, then 11.27 kilometers are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equivalent to how many miles? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 1.76 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5.9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 7.0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 8.4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 16.1 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is (C). The question essentially asks, “ 3 is to 4.83 as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 w hat is to 11.27?” Set up a proportion, then solve for x by the 2 2 12345678901234567890123456789012123456789012345678901 cross-product method: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 x 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 4.83 11.27 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~4.83!~x ! 5 ~3!~11.27! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~3!~11.27! 2 12345678901234567890123456789012123456789012345678901 x 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4.83 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 33.81 2 12345678901234567890123456789012123456789012345678901 , or 7 x 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4.83 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N otice that, despite all the intimidating decimal numbers, the solution 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 turns out to be a tidy number: 7. That’s typical of the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 205

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Arithmetic Mean (Simple Average), Median, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Mode, and Range 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Arithmetic mean (simple average), median, mode, and range are four 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 different ways to describe a set of terms quantitatively. H ere’s the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 definition of each one: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 arithmetic mean (average): In a set of n measurements, the sum of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measurements divided by n 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 median: The middle measurement after the measurements are ordered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by size (or the average of the two middle measurements if the number 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 of measurements is odd) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mode: The measurement that appears most frequently in a set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 range: The difference between the greatest measurement and the least 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measurement 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For example, given a set of six measurements, {8,24,8,3,2,7}: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 mean 5 4 (8 2 4 1 8 1 3 1 2 1 7) 4 6 5 24 4 6 5 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 median 5 5 The average of 3 and 7—the two middle measure2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ments in the set ordered in this way: {24,2,3,7,8,8} 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 mode 5 8 8 appears twice (more frequently than any other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measurement) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 range 5 12 The difference between 8 and 24 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the same set of values, the mean (simple average) and the median can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be, but are not necessarily, the same. For example: The set {3,4,5,6,7} has 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both a mean and median of 5. H owever, the set {22,0,5,8,9}has a mean of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 but a median of 5. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The GM AT covers arithmetic m ean far more frequently than median, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mode, or range, so let’s focus on problems involving mean. First of all, in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 finding a simple average, be sure the numbers being added are all of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same form or in terms of the same units. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 206 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 What is the average of , 25% , and .09? 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. .18 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 20% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. .32 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 The correct answer is A. Since the answer choices are not all expressed 2 2 12345678901234567890123456789012123456789012345678901 in the same form, first rewrite numbers as whichever form you think 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would be easiest to work with when you add the numbers together. In this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 case, the easiest form to work with is probably the decimal form. So, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rewrite the first two numbers as decimals, and then find the sum of the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three numbers: .20 1 .25 1 .09 5 .54. Finally, divide by 3 to find the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average: .54 4 3 5 .18. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To find a missing number when the average of all the numbers in a set is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 given, plug into the arithmetic-mean formula all the numbers you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know—which include the average, the sum of the other numbers, and the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 number of terms. Then, use algebra to find the missing number. O r, you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 can try out each answer choice, in turn, as the missing number until you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find one that results in the average given. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The average of five numbers is 26. Four of the numbers are –12, 90, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 –26, and 10. What is the fifth number? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 42 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 44 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 68 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 84 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 207

Part III: Q uantitative A bility

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Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. To solve the problem algebraically, let x 5 the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 missing number. Set up the arithmetic-mean formula, then solve for x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~90 1 10 2 12 2 26! 1 x 2 12345678901234567890123456789012123456789012345678901 26 5 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 62 1 x 2 12345678901234567890123456789012123456789012345678901 26 5 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 130 5 62 1 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 68 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 O r, you can try out each answer choice in turn. Start with the middle value, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 44 (choice (C)). The sum of 44 and the other four numbers is 106. Dividing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this sum by 5 gives you 21.2—a number less than the average of 26 that 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re aiming for. So you know the fifth number is greater than 44—and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that leaves choices (D) and (E). Try out the number 68 (choice (D)), and 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you’ll obtain the average of 26. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Remember: numerical answer choices are listed in ascending order of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 value. So, when working backward from numerical answer choices, start 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with choice (C), which is the median value. If (C) is either too great or too 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 less, you’ve narrowed down the options to two: (A) and (B) or (D) and 2 2 12345678901234567890123456789012123456789012345678901 (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If the numbers are easy to work with, you might be able to determine a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 missing term, given the simple average of a set of numbers, without 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 resorting to algebra. Simply apply a dose of logic. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If the average of six consecutive multiples of 4 is 22, what is the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 greatest of these integers? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 22 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 24 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 26 2 12345678901234567890123456789012123456789012345678901 D. 28 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 32 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. You can answer this question with common 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sense—no algebra required. Consecutive multiples of 4 are 4, 8, 12, 16,. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 . . . Given that the average of six such numbers is 22, the two middle terms 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (the third and fourth terms) must be 20 and 24. (Their average is 22.) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Accordingly, the fifth term is 28, and the sixth and greatest term is 32. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 208 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Arithmetic Series 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In an arithm etic series of numbers, there is a constant (unchanging) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difference between successive numbers in the series. In other words, all 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers in an arithmetic series are evenly spaced. All of the following are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples of an arithmetic series: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Successive integers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Successive even integers 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Successive odd integers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Successive multiples of the same number 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Successive integers ending in the same digit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 O n the GM AT, questions involving an arithmetic series might ask for the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 average or the sum of a series. When the numbers to be averaged form an 2 2 12345678901234567890123456789012123456789012345678901 arithmetic (evenly spaced) series, the average is simply the median (the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 middle number or the average of the two middle numbers if the number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms is even). In other words, the mean and median of the set of numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are the same. Faced with calculating the average of a long series of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evenly-spaced integers, you can shortcut the addition. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What is the average of the first 20 positive integers? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 7 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 10 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 15 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 20 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Since the terms are evenly spaced, the average 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is halfway between the 10th and 11th terms—which happen to be the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 integers 10 and 11. So, the average is 10 . (This number is also the 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 median.) If you take the average of the first term (1) and the last term (20), 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you get the same result: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 1 20 21 1 2 12345678901234567890123456789012123456789012345678901 5 , or 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Finding the sum (rather than the average) of an arithmetic (evenly spaced) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 series of numbers requires only one additional step: multiplying the 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 209

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 average (which is also the median) by the number of terms in the series. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The trickiest aspect of this type of question is determining the number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms in the series. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What is the sum of all odd integers between 10 and 40? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A. 250 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 325 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 375 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. 400 2 12345678901234567890123456789012123456789012345678901 2 E. 450 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The correct answer is C. The average of the described numbers is 25— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 halfway between 10 and 40 (in other words, half the sum of 10 and 40). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The number of terms in the series is 15. (The first term is 11, and the last 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 term is 39.) The sum of the described series of integers 5 25 3 15 5 375. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When calculating the average or sum of a series of evenly-spaced 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers, be careful when counting the number of terms in the series. For 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 instance, the number of positive odd integers less than 50 is 25, but the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of positive even integers less than 50 is only 24. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Permutations 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A perm utation is an arrangement of objects in which the order (sequence) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is important. Each arrangement of the letters A, B, C, and D, for example, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is a different permutation of the four letters. There are two different ways 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to determine the number of permutations for a group of objects. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. List all the permutations, using a methodical process to make sure 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you don’t overlook any. For the letters A, B, C, and D, start with A in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the first position, then list all possibilities for the second position, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 along with all possibilities for the third and fourth positions (you’ll 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discover six permutations): 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ABCD AC BD AD BC 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ABDC ACDB AD CB 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Placing B in the first position would also result in 6 permutations. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The same applies to either C or D in the first position. So the total 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number of permutations is 6 3 4 5 24. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 210 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Use the following formula (let n 5 the number of objects, and limit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the number of terms to the counting numbers, or positive integers): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N umber of permutations 5 n(n 2 1)(n 2 2)(n 2 3) . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The number of permutations can be expressed as n! (“ n factorial” ). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Using the factorial formula is much easier than compiling a list of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 permutations. For example, try applying the formula to the letters A, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B, C, and D: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4! 5 4(4 2 1)(4 2 2)(4 2 3) 5 4 3 3 3 2 3 1 5 24 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Five tokens—one red, one blue, one green, and two white—are 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 arranged in a row, one next to another. If the two white tokens are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 next to each other, how many arrangements according to color are 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 20 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 24 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 30 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is (D). The two white tokens might be in positions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1 and 2, 2 and 3, 3 and 4, or 4 and 5. For each of these four possibilities, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 there are 6 possible color arrangements (3!) for the other three tokens 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (which all differ in color). Thus, the total number of possible arrangements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is 4 3 6, or 24. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can shortcut common factorial calculations by memorizing them: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 3! 5 6, 4! 5 24, and 5! 5 120. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Combinations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A com bination is a group of certain objects selected from a larger set. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The order of objects in the group is not important. You can determine 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the total number of possible combinations by listing the possible groups 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in a methodical manner. For instance, to determine the number of 2 2 12345678901234567890123456789012123456789012345678901 possible three-letter groups among the letters A, B, C, D, and E, work 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 methodically, starting with A as a group member paired with B, then C, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then D, then E. Be sure not to repeat combinations (repetitions are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indicated in parentheses here). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 211

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A, B, C (A, C, B) (A, D, B) (A, E, B) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A, B, D A, C, D (A, D, C) (A, E, C) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A, B, E A, C, E A, D, E (A, E, D) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that each parenthesized combination backtracks to an earlier 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 letter. So, to be sure you don’t repeat any combination, make sure you 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 don’t backtrack to an earlier object. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Perform the same task assuming B is in the group, then assuming C is in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group (all combinations not listed here repeat what’s already listed). 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C, D, E B, C, D 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B, C, E 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B, D, E 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The total number of combinations is 10. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ow many two-digit numbers can be formed from the digits 1 2 12345678901234567890123456789012123456789012345678901 2 through 9, if no digit appears twice in a number? 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 36 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 72 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 81 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 144 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 162 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. Each digit can be paired with any of the other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 digits. To avoid double counting, account for the possible pairs as 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 follows: 1 and 2–9 (8 pairs), 2 and 3–9 (7 pairs), 3 and 4–9 (6 pairs), and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 so forth. The total number of distinct pairs is 8 1 7 1 6 1 5 1 4 1 3 1 2 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1 1 5 36. Since the digits in each pair can appear in either order, the total 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number of possible two-digit numbers is 2 3 36, or 72. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can approach combination problems as probability problems as well. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Why? You can think of the “ probability” of any single combination as 2 2 12345678901234567890123456789012123456789012345678901 “ one divided by” the total number of combinations (a fraction between 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 zero and 1). Use whichever method is quickest for the question at hand. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The topic of probability is next. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 212 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Probablility 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Probability refers to the statistical chances, of an event occurring (or not 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occurring). By definition, probability ranges from 0 to 1. (Probability is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 never negative, and it’s never greater than 1.) H ere’s the basic formula for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determining probability: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 number of ways the event can occur 2 12345678901234567890123456789012123456789012345678901 Probability 5 2 12345678901234567890123456789012123456789012345678901 total number of possible occurrences 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 If you randomly select one candy from a jar containing two cherry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 candies, two licorice candies, and one peppermint candy, what is 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the probability of selecting a cherry candy? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 B. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. There are two ways among five possible 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 occurrences that a cherry candy will be selected. Thus, the probability of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 selecting a cherry candy is . 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To calculate the probability of an event N O T occurring, just subtract 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the probability of the event occurring from 1. So, referring to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 preceding question, the probability of N O T selecting a cherry candy is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 2 12345678901234567890123456789012123456789012345678901 . (Subtract from 1.) 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 213

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This N ext Level focuses first on the following specific applications of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 fractions, percents, decimals, ratios, and proportion (with special empha- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sis on how the test-makers incorporate algebraic features into GM AT 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions covering these concepts): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Altering fractions and ratios 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Ratios involving more than two quantities 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Proportion problems with variables 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext, you’ll explore how the test-makers design tougher-than-average 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions involving the following topics (all of which we’ve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 covered in this chatper except the second and third topics listed here): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Arithmetic mean (simple average) and median (two ways that a set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of numbers can be measured as a whole) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Standard deviation (a quantitative expression of the dispersion of a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set of measurements) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Geometric series (the pattern from one number to the next in an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exponential sequence of numbers) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Permutations (the possibilities for arranging a set of objects) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Combinations (the possibilities for selecting groups of objects from 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a set) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Probability (the statistical chances of a certain event, permutation, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or combination occurring) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Altering Fractions and Ratios 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An average test-taker might assume that adding the same positive quantity 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to a fraction’s numerator (p) and to its denominator (q) leaves the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 12345678901234567890123456789012123456789012345678901 unchanged. But this is true if and only if the original 2 fraction’s value 2 12345678901234567890123456789012123456789012345678901 q 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

SD

214

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 numerator and denominator were equal to each other. O therwise, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fraction’s value will change. Remember the following three rules, which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 apply to any positive numbers x , p, and q (the first one is the no-brainer 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 you just read): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 p p 1 x 2 12345678901234567890123456789012123456789012345678901 If p 5 q, then 5 . (The fraction’s value remains unchanged and 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 q q1x 2 12345678901234567890123456789012123456789012345678901 is always 1.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 p p1x 2 12345678901234567890123456789012123456789012345678901 If p . q, then . . (The fraction’s value will decrease.) 2 12345678901234567890123456789012123456789012345678901 q q1x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 p p1x 2 12345678901234567890123456789012123456789012345678901 , . (The fraction’s value will increase.) If p , q, then 2 12345678901234567890123456789012123456789012345678901 q q1x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to alter a ratio by adding or subtracting 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from one (or both) terms in the ratio. The rules for altering ratios are the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 same as for altered fractions. In either case, set up a proportion and solve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebraically for the unknown term. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A drawer contains exactly half as many white shirts as blue shirts. If 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four more shirts of each color are added to the drawer, the ratio of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 blue to white shirts would be 8:5. H ow many blue shirts does the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 drawer contain? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 14 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 11 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 10 2 12345678901234567890123456789012123456789012345678901 2 E. 9 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is B. Represent the original ratio of white to blue 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 shirts by the fraction , where x is the number of white shirts, then add 4 2 2 12345678901234567890123456789012123456789012345678901 2x 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to both the numerator and denominator. Set this fraction equal to (the 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 ratio after adding shirts). Cross-multiply to solve for x : 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 14 5 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2x 24 8 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8x 1 32 5 10x 1 20 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 5 2x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 56 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The original denominator is 2x , or 12. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 215

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When you add (or subtract) the same number from both the numerator 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and denominator of a fraction—or from each term in a ratio—you alter 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 the fraction or ratio—unless the original ratio was 1:1 (in which case the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ratio goes unchanged). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Ratios Involving More than Two Quantities 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You approach ratio problems involving three or more quantities the same 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 way as those involving only two quantities. The only difference is that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 there are more “ parts” that make up the “ whole.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Three lottery winners—X , Y , and Z —are sharing a lottery jackpot. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 X ’s share is of Y ’s share and of Z ’s share. If the total jackpot is 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $195,000, what is the dollar amount of Z ’s share? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. $15,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $35,000 2 12345678901234567890123456789012123456789012345678901 C. $75,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. $105,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $115,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. At first glance, this problem doesn’t appear to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involve ratios. (Where’s the colon?) But it does. The ratio of X ’s share to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Y ’s share is 1:5, and the ratio of X ’s share to Z ’s share is 1:7. So you can set 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 up the following triple ratio: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 X :Y :Z 5 1:5:7 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 X ’s winnings account for 1 of 13 equal parts (1 1 5 1 7) of the total 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 jackpot. of $195,000 is $15,000. Accordingly, Y ’s share is 5 times 2 2 12345678901234567890123456789012123456789012345678901 13 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that amount, or $75,000, and Z ’s share is 7 times that amount, or 2 2 12345678901234567890123456789012123456789012345678901 $105,000. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In handling word problems involving ratios, think of a whole as the sum 2 2 12345678901234567890123456789012123456789012345678901 of its fractional parts, as in the method used to solve the preceding 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 5 7 12345678901234567890123456789012123456789012345678901 problem: (X ’s share) 1 (Y ’s share) 1 (Z ’s share) 5 1 (the whole 2 2 12345678901234567890123456789012123456789012345678901 13 13 13 2 12345678901234567890123456789012123456789012345678901 jackpot). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 216 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Proportion Problems with Variables 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT proportion question might use letters instead of numbers—to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 focus on the process rather than the result. You can solve these problems 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebraically or by using the plug-in strategy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A candy store sells candy only in half-pound boxes. At c cents per 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 box, which of the following is the cost of a ounces of candy? [1 2 12345678901234567890123456789012123456789012345678901 pound 5 16 ounces] 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 c 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 16c 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. ac 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ac 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 8c 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. This question is asking: “ c cents is to one box 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 as how m any cents are to a ounces?” Set up a proportion, letting x equal 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the cost of a ounces. Because the question asks for the cost of ounces, 2 12345678901234567890123456789012123456789012345678901 convert 1 box to 8 ounces (a half pound). Use the cross-product method to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solve quickly: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 c x 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 8 a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8x 5 ca 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ca 2 12345678901234567890123456789012123456789012345678901 x 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can also use the plug-in strategy for this question—either instead of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebra or, better yet, to check the answer you chose using algebra. Pick 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 easy numbers to work with, such as 100 for c and 8 for a. At 100 cents per 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8-ounce box, 8 ounces of candy costs 100 cents. Plug in your numbers for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a and c into each answer choice. O nly choice (D) gives you the number 100 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re looking for. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 217

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Simple Average and Median 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For any set of terms, the arithm etic m ean (A M ), also called the sim ple 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average, is the sum of the terms (a 1 b 1 c 1 . . .) divided by the number of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms (n) in the set. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~a 1 b 1 c 1 . . .! 2345678901234567890123456789012123456789012345678901 2 1 AM 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 O n the GM AT, easier questions involving simple average might ask you to 2 2 12345678901234567890123456789012123456789012345678901 add numbers together and divide a sum. A tougher question might ask you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to perform one or both of these tasks (both of which involve algebra): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Find the value of a number that changes an average from one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number to another express simple average in terms of variables 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 instead of just numbers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • When an additional number is added to a set, and the average of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the numbers in the set changes as a result, you can determine the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value of the number that’s added by applying the arithmetic-mean 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 formula twice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The average of three numbers is 24. If a fourth number is added, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the arithmetic mean of all four numbers is 21. What is the fourth 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 210 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 16 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. To solve the problem algebraically, first 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine the sum of the three original numbers by the arithmetic-mean 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formula: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a1b1c 2 12345678901234567890123456789012123456789012345678901 24 5 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, apply the formula again accounting for the additional (fourth) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 number. The new average is 21, the sum of the other three numbers is –12, 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and the number of terms is 4. Solve for the missing number (x ): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 212 1 x 2 12345678901234567890123456789012123456789012345678901 21 5 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 24 5 212 1 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 85x 2 218 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Take It to the Next Level

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 You approach arithmetic-mean problems that involve variables instead of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (or in addition to) numbers in the same way as those involving only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers. Just plug-in the information you’re given to the arithmetic-mean 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 formula, and then solve the problem algebraically. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If A is the average of P, Q , and another number, which of the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 following represents the missing number? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 3A 2 P 2 Q 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. A 1 P 1 Q 2 12345678901234567890123456789012123456789012345678901 2 C. 3A 2 P 1 Q 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. A 2 P 1 Q 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. 3A 2 P 1 Q 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Let x 5 the missing number. Solve for x by the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 arithmetic-mean formula: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 P1Q 1x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A5 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3A 5 P 1 Q 1 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3A 2 P 2 Q 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Should you try using the plug-in strategy to solve this problem, testing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each answer choice by substituting simple numbers for P, Q , and A ? N o; 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 it’s too complex. So you’ll need to be flexible. Try using shortcuts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wherever you can, but recognize their limitations. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Standard Deviation 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Standard deviation is a measure of dispersion among members of a set. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Computing standard deviation involves these steps: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Compute the arithmetic mean (simple average) of all terms in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the set. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Compute the difference between the mean and each term. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Square each difference you computed in step (2). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Compute the mean of the squares you computed in step (3). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. Compute the non-negative square root of the mean you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 computed in step (4). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 219

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For example, here’s how you’d determine the standard deviation of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Distribution A : {21, 2, 3, 4}: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 21 1 2 1 3 1 4 8 2 12345678901234567890123456789012123456789012345678901 1. Arithmetic mean 5 2 5 5 2. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The difference between the mean (2) and each term: 2 2 (21) 5 3; 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 2 2 5 0; 3 2 2 5 1; 4 2 2 5 2. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 2 12345678901234567890123456789012123456789012345678901 , 0 , 1 , 2 } 5 {9, 0, 1, 4} 3. The square of each difference: {3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9 1 0 1 1 1 4 14 7 2 12345678901234567890123456789012123456789012345678901 4. The mean of the squares: 5 5 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 4 4 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 The standard deviation of Distribution A 5 5. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to calculate standard deviation (as in the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 preceding example). O r, a question might ask you to com pare standard 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deviations. You might be able to make the comparison without precise 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculations—by remembering to the follow this general rule: T he greater 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the data are spread aw ay from the m ean, the greater the standard 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deviation. For example, consider these two distributions: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Distribution A : {1, 2.5, 4, 5.5, 7} 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Distribution B: {1, 3, 4, 5, 7} 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In both sets, the mean and median is 4, and the range is 6. But the standard 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deviation of A is greater than that of B, because 2.5 and 5.5 are further 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 away than 3 and 5 from the mean. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Which of the following distributions has the greatest standard 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deviation? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. {–1, 1, 3} 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. {1, 2, 5} 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. {0, 4, 5} 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. {–3, –1, 2} 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. {2, 3, 6} 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. N otice that in each of the choices (A), (B), and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (E), the distribution’s range is 4, but that in choice (C) and choice (D), the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 range is 5. So, the correct answer is probably either (C) or (D). Focusing on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these two choices, notice that the middle term in choice (C), 4, is skewed 2 2 12345678901234567890123456789012123456789012345678901 further away from the mean than the middle term in choice (D). That’s a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 good indication that (C) provides the distribution having the greatest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 standard deviation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 220 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Î

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Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

S D

S D

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Geometric Series 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In a geom etric series of numbers, each term is a constant multiple of the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 preceding one; in other words, the ratio between any term and the next 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one is constant. The multiple (or ratio) might be obvious by examining the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 series—for example: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 In the geometric series 2, 4, 8, 16, . . . , you can easily determine that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the constant multiple is 2 (and the ratio of each term to the next is 1:2). 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the geometric series 1, 23, 9, 227, . . . , you can easily determine 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the constant multiple is 23 (and the ratio of each term to the next 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is 1:23). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nce you know the multiple (or ratio), you can answer any question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 asking for an unknown term—or for either the sum or the average of 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 certain terms. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In a geometric series, each term is a constant multiple of the 2 12345678901234567890123456789012123456789012345678901 2 preceding one. If the third and fourth numbers in the series are 8 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and 216, respectively, what is the first term in the series? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 232 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 4 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 4 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 64 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. The constant multiple is 22. But since you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 need to work backward from the third term (8), apply the reciprocal of 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 that multiple twice. The second term is ~8! 2 5 24. The first term is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 ~24! 2 5 2. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 221

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In a geometric series, each term is a constant multiple of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 preceding one. What is the sum of the first four numbers in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 geometric series whose second number is 4 and whose third 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 number is 6? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 16 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 19 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 22 2345678901234567890123456789012123456789012345678901 2 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 21 2345678901234567890123456789012123456789012345678901 2 1 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 20 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 The correct answer is D. The constant multiple is . In other words, the 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ratio of each term to the next is 3:2. Since the second term is 4, the first 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 8 12345678901234567890123456789012123456789012345678901 term is 4 3 5 . Since the third term is 6, the fourth term is 6 3 5 2 2 12345678901234567890123456789012123456789012345678901 3 3 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 18 8 2 2 12345678901234567890123456789012123456789012345678901 , or 9. The sum of the four terms 5 1 4 1 6 1 9 5 21 . 2 12345678901234567890123456789012123456789012345678901 2 3 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can’t calculate the average of terms in a geometric series simply by 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 averaging the first and last term in the series. That’s because the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 progression is geometric, not arithmetic. Instead, you need to add up the 2 2 12345678901234567890123456789012123456789012345678901 terms, then divide by the number of terms. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 You can also solve geometric series problems by applying a special 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 formula. But you’ll need to memorize it because the test won’t provide it. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In the following formula, r 5 the constant multiple (or the ratio between 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each term and the preceding one), a 5 the first term in the series, n 5 the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position number for any particular term in the series, and T 5 the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 particular term itself: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ar(n 2 1) 5 T 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can solve for any of the formula’s variables, as long as you know the 2 2 12345678901234567890123456789012123456789012345678901 values for the other three. Following are two examples: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a 5 3 and r 5 2, then the third term 5 (3)(2)2 5 12, and the sixth 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 term 5 (3)(2) 5 (3)(32) 5 96. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 222 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 If the sixth term is 2 and the constant ratio is , then the first term 2 12345678901234567890123456789012123456789012345678901 16 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (a) 5 22: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 a 5 2 2 12345678901234567890123456789012123456789012345678901 2 16 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 5 2 a 2345678901234567890123456789012123456789012345678901 2 1 32 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 ~32! 5 22 a 2 1 2 12345678901234567890123456789012123456789012345678901 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The algebra is simple enough—but you need to know the formula, of 2 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 course. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In a geometric series, each term is a constant multiple of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 preceding one. If the first three terms in a geometric series are 22, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x , and 28, which of the following could be the sixth term in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 series? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 24,096 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 21,024 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 512 2 12345678901234567890123456789012123456789012345678901 D. 1,024 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 2,048 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is E. Since all pairs of successive terms must have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 x 2 12345678901234567890123456789012123456789012345678901 2 the same ratio, 5 . By the cross-product method, x 5 16, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 28 2 12345678901234567890123456789012123456789012345678901 hence x 5 64. Applying the formula you just learned, for 14, the sixth 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 term would be (22)(4) 5 22,048, while for 24 it would be 2,048. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Permutations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A perm utation is an arrangement of objects in which the order (sequence) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is important. Each arrangement of the letters A, B, C, and D, for example, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is a different permutation of the four letters. There are two different ways 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to determine the number of permutations for a group of distinct objects. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. List all the permutations, using a methodical process to make sure 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you don’t overlook any. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 223

SD SD

Take It to the Next Level

S D

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Use the following formula (let n 5 the number of objects) and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 limit the number of terms to the counting numbers, or positive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 integers: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 N umber of permutations 5 n(n 2 1)(n 2 2)(n 2 3) . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For example, the number of arrangements (permutations) of the four 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 letters A, B, C, and D is 4! 5 4 3 3 3 2 3 1 5 24. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To handle a tougher permutation question, you might need to calculate 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 multiple permutations, then add them together—applying a dose of logic 2 2 12345678901234567890123456789012123456789012345678901 2 along the way. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Five children—two boys and three girls—are standing in a single2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 file line. If the first in line is a girl, how many different arrange2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ments of the five children are possible? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 20 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 36 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 45 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 72 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. Label the five children B1, B2, G1, G2, and G3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If G1 is first in line, with the other four children in any order, the number 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of permutations is 4!, or 24. The same applies to either G2 or G3 in the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 first position. So the total number of permutations is 4! 1 4! 1 4! 5 72. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Combinations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A com bination is a group of certain objects selected from a larger set. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 order of objects in the group is not important. You can determine the total 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of possible combinations by listing the possible groups in a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 methodical manner. O n the GM AT, a simple combination question will 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involve the selection of one or more objects from one larger set. A more 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 complex combination question might require you to determine the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number of combinations involving tw o or m ore sets of objects. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 224 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 From a group of three violinists and four pianists, a judge must 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 select two violinists and two pianists to perform at a music recital. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow many different combinations of musicians might perform at 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the recital? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 9 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 24 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. 30 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is C. The judge must select two of three violinists, 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 for a total of three possible combinations. The judge must select two of 2 2 12345678901234567890123456789012123456789012345678901 four pianists, for a total of six possible combinations. For each pair of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 violinists, there are six possible pairs of pianists. Thus, the total number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four-musician combinations is 6 3 3 5 18. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A combination question might also incorporate a permutation feature, 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 making it even more challenging. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 From a group of three singers and three comedians, a show 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 organizer must select two singers and two comedians to appear one 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 after another in a show. H ow many different ways can the orga2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nizer arrange performers for the show? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 72 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 90 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 136 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 180 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 216 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The organizer must select two of three singers, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 for a total of 3 possible combinations. Similarly, the judge must select two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of three comedians, for a total of 3 possible combinations. For each pair of 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 singers, there are 3 possible pairs of comedians. Thus, the total number of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 four-performer combinations is 3 3 3, or 9. The four performers can 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 appear in any order in the show. So, for each four-performer combination, 2 12345678901234567890123456789012123456789012345678901 there are 24 permutations (4!, or 4 3 3 3 2 3 1). The total number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible arrangements, then, is 24 3 9, or 216. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 225

Part III: Q uantitative A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Probability 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the basic formula for determining the probability of an event 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 occurring: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of ways the event can occur 2 12345678901234567890123456789012123456789012345678901 Probability 5 2 12345678901234567890123456789012123456789012345678901 total number of possible occurrences 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For example, a standard deck of 52 playing cards contains 12 face cards. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 3 2345678901234567890123456789012123456789012345678901 1 The probability of selecting a face card from a standard deck is , or . 2 2 12345678901234567890123456789012123456789012345678901 52 13 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, a tougher probability question will involve this basic 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 formula, but will also add a complication of some kind. It might require 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you to determine any of the following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Certain missing facts needed for a given probability 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Probabilities involving two (or more) independent events 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Probabilities involving an event that is dependent on another event 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Think twice before you try to “ intuit” the answer for these three types of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probability questions. Probabilities involving complex scenarios such as 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 these are often greater or less than you might expect. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Missing Facts Needed for a Given Probability 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this question type, instead of calculating probability, you determine 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what missing number is needed for a given probability. Don’t panic; just 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 plug what you know into the basic formula, and solve for the missing 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A piggy-bank contains a certain number of coins, of which 53 are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dimes and 19 are nickels. The remainder of the coins in the bank 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 are quarters. If the probability of selecting a quarter from this bank 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 is , how many quarters does the bank contain? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 30 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 27 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 24 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 16 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 226 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Tip

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. O n its face, this question looks complicated, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but it’s really not. Just plug what you know into the probability formula. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Let x 5 the number of quarters in the bank (this is the numerator of the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 formula’s fraction), and let x 1 72 5 the total number of coins (the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fraction’s denominator). Then solve for x (use the cross-product method to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear fractions): 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 x 2 12345678901234567890123456789012123456789012345678901 5 2345678901234567890123456789012123456789012345678901 2 1 4 x 1 72 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 1 72 5 4x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 72 5 3x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 24 5 x 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Probability Involving Two (or More) Independent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Events 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Two events are independent if neither event affects the probability that the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 other will occur. (You’ll look at dependent events a few pages ahead.) O n 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the GM AT, look for either of these scenarios involving independent events: 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The random selection of one object from each of tw o or m ore 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 groups 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The random selection of one object from a group, then replacing it 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and selecting again (as in a “ second round” or “ another turn” of a 2 2 12345678901234567890123456789012123456789012345678901 game) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In either scenario, the simplest calculation involves finding the probability 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of two events both occurring. All you need to do is multiply together their 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 individual probabilities: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (probability of event 1 occurring) 3 (probability of event 2 occurring) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 (probability of both events occurring) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For example, assume that you randomly select one letter from each of two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 12345678901234567890123456789012123456789012345678901 sets: {A,B} and {C,D,E}. The probability of selecting A and C 5 3 , 2 2 12345678901234567890123456789012123456789012345678901 2 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 or . 2 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To calculate the probability that two events will not both occur, subtract 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from 1 the probability of both events occurring. To determine the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probability that three events will all occur, just multiply the third event’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 probability by the other two. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 227

Part III: Q uantitative A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If one student is chosen randomly out of a group of seven students, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then one student is again chosen randomly from the same group of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 seven, what is the probability that two different students will be 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 chosen? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 36 2 12345678901234567890123456789012123456789012345678901 A. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 49 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 B. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 19 2 12345678901234567890123456789012123456789012345678901 C. 2345678901234567890123456789012123456789012345678901 2 1 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13 2 12345678901234567890123456789012123456789012345678901 D. 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 14 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 48 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 49 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. You must first calculate the chances of picking 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the sam e student tw ice by multiplying together the two individual 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 1 2 12345678901234567890123456789012123456789012345678901 probabilities for the student: 3 5 . The probability of picking the 2 12345678901234567890123456789012123456789012345678901 7 7 49 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same student twice, added to the probability of not picking the same 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 student twice, equals 1. So to answer the question, subtract from 1. 2 12345678901234567890123456789012123456789012345678901 49 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In one selection, the probability of not selecting a certain student from the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 group of seven is (the probability of selecting the student, subtracted 2 12345678901234567890123456789012123456789012345678901 7 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from 1). But does this mean that the probability of not selecting the same 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 6 36 2 12345678901234567890123456789012123456789012345678901 student twice 5 3 5 ? N o! M ake sure you understand the 2 12345678901234567890123456789012123456789012345678901 7 7 49 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 difference. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Probability Involving a Dependent Event 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Two distinct events might be related in that one event affects the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probability of the other one occurring — for example, randomly selecting 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one object from a group, then selecting a second object from the same 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group w ithout replacing the first selection. Removing one object from the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group increases the odds of selecting any particular object from those that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remain. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You handle this type of problem as you would any other probability 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem: Calculate individual probabilities, then combine them. 2 1 2 228 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 6: M ath Review—N umber Forms, Relationships, and Sets

Alert!

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In a random selection of two people from a group of five—A, B, C, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D, and E—what is the probability of selecting A and B? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 D. 2 12345678901234567890123456789012123456789012345678901 15 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 20 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. You need to consider each of the two selections 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 separately. In the first selection, the probability of selecting either A or B is 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 . But the probability of selecting the second of the two is —because after 2 2 12345678901234567890123456789012123456789012345678901 5 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the first selection only four people remain from whom to select. Since the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 question asks for the probability of selecting both A and B (as opposed to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 1 2 12345678901234567890123456789012123456789012345678901 either one), multiply the two individual probabilities: 3 5 5 . 2 12345678901234567890123456789012123456789012345678901 5 4 20 10 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can also approach a question such as this one as a com bination 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem. For this question, here are all the possibilities: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A and either B, C, D, or E (4 combinations) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B and either C, D, or E (3 combinations) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C and either D or E (2 combinations) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D and E (1 combination) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 There are 10 possible combinations, so the probability of selecting A and B 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is 1 in 10. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Strategies such as plugging-in test numbers, working backwards, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 even sizing up the answer choices don’t work for most probability 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 questions (including the preceding one). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 229

Chapter

7 Math Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this chapter, first you’ll broaden your arithmetical horizons by dealing 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with numbers in more abstract, theoretical settings. You’ll examine the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following topics: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The concept of absolute value 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • N umber signs and integers—and what happens to them when you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 apply the four basic operations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Factors, multiples, divisibility, prime numbers, and the “ prime 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factorization” method 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The rules for combining exponential numbers (base numbers and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ powers” ) using the four basic operations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The rules for combining radicals using the four basic operations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The rules for simplifying terms containing radical signs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, you’ll review the following basic algebra skills: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Solving a linear equation in one variable 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Solving a system of two equations in two variables—by substitu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion and by addition-subtraction 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognizing unsolvable linear equations when you see them 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • H andling algebraic inequalities 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Basic Properties of Numbers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll begin this chapter by reviewing the basics about integers, number 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 signs (positive and negative), and prime numbers. First, make sure you’re 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 up to speed on the following definitions, which you’ll need to know for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this chapter as well as for the test: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 230

Alert!

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Absolute value (of a real number): The number’s distance from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 zero (the origin) on the real-number line. The absolute value of x is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indicated as |x |. (The absolute value of a negative number can be 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 less than, equal to, or greater than a positive number.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Integer: Any non-fraction number on the number line: {. . . 23, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 22, 21, 0, 1, 2, 3, . . .}. Except for the number zero (0), every 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 integer is either positive or negative. Every integer is either even or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 odd. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Factor (of an integer n): Any integer that you can multiply by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another integer for a product of n. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Prime number: Any positive integer that has exactly two positive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factors: 1 and the number itself. In other words, a prime number is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not divisible by (a multiple of) any positive integer other than itself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and 1. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The factors of any integer n include 1 as well as n itself. Z ero (0) and 1 are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not prime numbers; 2 is the first prime number. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Number Signs and the Four Basic Operations 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The four basic operations are addition, subtraction, multiplication, and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 division. Be sure you know the sign of a number that results from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 combining numbers using these operations. H ere’s a table that includes all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the possibilities (a “ ?” indicates that the sign depends on which number 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 has the greater absolute value): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Addition Subtraction Multiplication Division 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ~1! 1 ~1! 5 1 ~1! 2 ~2! 5 ~1! ~1! 3 ~1! 5 1 ~1! 4 ~1! 5 1 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ~2! 1 ~2! 5 2 ~2! 2 ~1! 5 ~2! ~1! 3 ~2! 5 2 ~1! 4 ~2! 5 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~1! 1 ~2! 5 ? ~1! 2 ~1! 5 ? ~2! 3 ~1! 5 2 ~2! 4 ~1! 5 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~2! 1 ~1! 5 ? ~2! 2 ~2! 5 ? ~2! 3 ~2! 5 1 ~2! 4 ~2! 5 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT problems involving combining numbers by addition or subtraction 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 usually incorporate the concept of absolute value, as well as the rule for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subtracting negative numbers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 231

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 |21 2 2| 2 |5 2 6| 2 |23 1 4| 5 ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 25 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 23 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 3 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 E. 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is C. First, determine each of the three absolute 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 values: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 |21 2 2| 5 |23| 5 3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 |5 2 6| 5 |21| 5 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 |23 1 4| 5 |1| 5 1 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Then combine the three results: 3 2 1 2 1 5 1. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Because multiplication (or division) involving two negative terms always 2 2 12345678901234567890123456789012123456789012345678901 2 results in a positive number: 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • M ultiplication or division involving any even number of negative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms gives you a positive number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • M ultiplication or division involving any odd number of negative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms gives you a negative number. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A number N is the product of seven negative numbers, and the 2 12345678901234567890123456789012123456789012345678901 number M is the product of six negative numbers and one positive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number. Which of the following holds true for all possible values of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M and N ? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 I. M 3 N , 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 II. M 2 N , 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 III. N 1 M , 0 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. I only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. II only 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. I and II only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. II and III only 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. I, II, and III 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The product of seven negative numbers is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 always a negative number. (M is a negative number.) The product of six 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 negative numbers is always a positive number, and the product of two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 positive numbers is always a positive number. (N is a positive number.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, the product of M and N must be a negative number; (I) is always 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 true. Subtracting a positive number N from a negative number M always 2 1 2 232 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 results in a negative number less than M ; (II) is always true. H owever, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whether (III) is true depends on the values of M and N . If |N | . |M |, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N 1 M . 0, but if |N | , |M |, then N 1 M , 0. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Integers and the Four Basic Operations 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 When you combine integers using a basic operation, whether the result is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an odd integer, an even integer, or a non-integer depends on the numbers 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 you combined. H ere’s a table that summarizes all the possibilities: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Addition and Subtraction 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 integer 6 integer 5 integer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 even integer 6 even integer 5 even integer 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 even integer 6 odd integer 5 odd integer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 odd integer 6 odd integer 5 even integer 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Multiplication and Division 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 integer 3 integer 5 integer 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 integer 4 non-zero integer 5 integer, but only if the numerator 2 12345678901234567890123456789012123456789012345678901 is divisible by the denominator (if the result is a quotient with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 no remainder) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 odd integer 3 odd integer 5 odd integer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 even integer 3 non-zero integer 5 even integer 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 even integer 4 2 5 integer 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 odd integer 4 2 5 non-integer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions that test you on the preceding rules sometimes look like 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 algebra problems, but they’re really not. Just apply the appropriate rule or, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 if you’re not sure of the rule, plug in simple numbers to zero-in on the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct answer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If P is an odd integer, and if Q is an even integer, which of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following expressions CAN N O T represent an even integer? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 3P 2 Q 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 3P 3 Q 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 2Q 3 P 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 3Q 2 2P 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 32P 2 2Q 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 233

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Since 3 and P are both odd integers, their 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 product (3P) must also be an odd integer. Subtracting an even integer (Q ) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from an odd integer results in an odd integer in all cases. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Factors, Multiples, and Divisibility 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Figuring out whether one number (f) is a factor of another (n) is no big 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 deal. Just divide n by f. If the quotient is an integer, then f is a factor of n 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 (and n is divisible by f). If the quotient is not an integer, then f is not a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factor of n, and you’ll end up with a rem ainder after dividing. For 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example, 2 is a factor of 8 because 8 4 2 5 4, which is an integer. O n the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 8 2 2 12345678901234567890123456789012123456789012345678901 other hand, 3 is not a factor of 8 because 8 4 3 5 , or 2 , which is a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 3 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 non-integer. (The remainder is 2.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Remember these basic rules about factors, which are based on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 definition of the term “ factor” : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. Any integer is a factor of itself. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. 1 and 21 are factors of all integers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. The integer zero has an infinite number of factors, but is not a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factor of any integer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. A positive integer’s greatest factor (other than itself) will never be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 greater than one half the value of the integer. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the “ flip side” of factors are multiples. If f is a factor of n, then n is a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiple of f. For example, 8 is a multiple of 2 for the same reason that 2 is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a factor of 8—because 8 4 2 5 4, which is an integer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you can see, factors, multiples, and divisibility are simply different 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 aspects of the same concept. So, a GM AT question about factoring is also 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 about multiples and divisibility. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 234 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If n . 6, and if n is a multiple of 6, which of the following is always 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a factor of n? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. n 2 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. n 1 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 2345678901234567890123456789012123456789012345678901 2 1 C. 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 2345678901234567890123456789012123456789012345678901 2 D. 1 13 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 n 12345678901234567890123456789012123456789012345678901 E. 2345678901234567890123456789012123456789012345678901 2 1 16 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Since 3 is a factor of 6, 3 is also a factor of any 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 positive-number multiple of 6. Thus, if you divide any multiple of 6 by 3, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the quotient will be an integer. In other words, 3 will be a factor of that 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 number (n). As for the incorrect choices, n 2 6 (choice A) is a factor of n 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 only if n 5 12. n 1 6 (choice (B)) can never be a factor of n because n 1 6 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is greater than n. With choice (D), you always end up with a remainder of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. You can eliminate choices (D) and (E) because the greatest factor of any 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 positive number (other than the number itself) is half the number, which in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 2 12345678901234567890123456789012123456789012345678901 this case is . 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Although the plug-in strategy works for the preceding question, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 should try out more than one sample value for n. If n 5 12, choices (A), 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (C), and (E) all are viable. But try out the number 18, and choice (C) is the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only factor of n. (To be on the safe side, you should try out at least one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional sample value as well, such as 24.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prime Numbers and Prime Factorization 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A prim e num ber is a positive integer that is divisible by (a multiple of) only 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 two positive integers: itself and 1. Just for the record, here are all the prime 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers less than 50: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2357 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 11 13 17 19 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 23 29 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 31 37 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 41 43 47 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Determining all the factors of great integers can be tricky; it’s easy to over- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 look some factors. To find all factors of a great number, use a method called 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 235

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 prim e factorization. Divide the number by each prime number in turn, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 starting with 2 and working up from there (2,3,5,7,11 . . . ), then try to find 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factors for the quotients as well, using the same method. Test prime num- 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 bers up to the point where your quotient is no greater than the greatest 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factor you’ve already found. For example, here’s how you apply prime 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factorization to the number 110 (prime-number quotients are shown in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 italics): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 110 4 2 5 55, and 55 5 5 3 11 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 110 4 3 5 non-integer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 110 4 5 5 22, and 22 5 2 3 11 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 110 4 7 5 non-integer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 110 4 11 (already covered) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The prime factor quotients are 2, 5, and 11, and their product is 110. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (That’s no coincidence.) T he product of all prim e-num ber quotients w ill 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 equal your original num ber. A number’s prime factorization refers to all its 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 prime factors multiplied together. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To find all other positive factors of a number, combine any two or more 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prime factors by multiplication. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Which of the following is a prime factorization of 144? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 2 4 3 3 2 2 12345678901234567890123456789012123456789012345678901 3 B. 4 3 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 C. 2 3 12 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 2 2 3 3 3 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 3 4 E. 2 3 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Divide 144 by its least possible prime factor, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which is 2. Continue to divide the result by 2, and you ultimately obtain 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a prime-number quotient: 144 4 2 5 72 4 2 5 36 4 2 5 18 4 2 5 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9 4 3 5 3. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Exponents (Powers) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An ex ponent, or pow er, refers to the number of times a number (referred 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to as the base num ber) is multiplied by itself, plus 1. In the number 2 3 , the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 base number is 2 and the exponent is 3. To calculate the value of 2 3 , you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiply 2 by itself twice: 2 3 5 2 3 2 3 2 5 8. 2 1 2 236 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, questions involving exponents usually require you to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combine two or more terms that contain exponents. To do so, you need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know some basic rules. Can you combine base numbers—using addition, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 subtraction, multiplication, or division—before applying exponents to the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers? The answer depends on which operation you’re performing. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Combining Exponents by Addition or Subtraction 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 When you add or subtract terms, you cannot combine base numbers or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exponents. It’s as simple as that. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x x x 2345678901234567890123456789012123456789012345678901 2 1 a 1 b Þ (a 1 b) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x x x a 2 b Þ (a 2 b) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If you don’t believe it, try plugging in a few easy numbers. N otice that you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 get a different result depending on which you do first: combine base 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers or apply each exponent to its base number: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 (3 1 4) 5 7 5 49 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 1 4 2 5 9 1 16 5 25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 2 12345678901234567890123456789012123456789012345678901 2 x 2 x 5 ? If x 5 22, then x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 270 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 258 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 234 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 4 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 26 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. You cannot combine exponents here, even 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 though the base number is the same in all three terms. Instead, you need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 apply each exponent, in turn, to the base number, then subtract: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 5 2 2 12345678901234567890123456789012123456789012345678901 x 2 x 2 x 5 (22) 2 (22) 2 (22) 5 232 2 4 1 2 5 234 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Combining Exponents by Multiplication or Division 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 It’s a whole different story for multiplication and division. First, remember 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 these two simple rules: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. You can combine base numbers first, but only if the exponents are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the same: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ax 3 b x 5 ~ab!x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 237

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. You can combine exponents first, but only if the base numbers are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the same. When multiplying these terms, add the exponents. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When dividing them, subtract the denominator exponent from 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 the numerator exponent: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x y ~x 1 y! 2 12345678901234567890123456789012123456789012345678901 a 3a 5a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 x a 2 12345678901234567890123456789012123456789012345678901 ~x 2 y! 5a 2 12345678901234567890123456789012123456789012345678901 y 2 12345678901234567890123456789012123456789012345678901 a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 When the same base number (or term) appears in both the numerator and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 denominator of a fraction, you can factor out, or cancel, the number of 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 powers common to both. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 3 2 12345678901234567890123456789012123456789012345678901 x y 2 12345678901234567890123456789012123456789012345678901 Which of the following is a simplified version of ? 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 3y 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 y 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 y 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 xy 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 E. x y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. The simplest approach to this problem is to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factor out, x 2 and y 2 from numerator and denominator. This leaves you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with x 1 in the denominator and y 1 in the numerator. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Canceling” a base number’s powers in a fraction’s numerator and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ax 2 12345678901234567890123456789012123456789012345678901 (x 2 y) 12345678901234567890123456789012123456789012345678901 denominator is actually a shortcut to applying the rule y 5 a along 2 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2x 2 12345678901234567890123456789012123456789012345678901 with another rule, a 5 x , that you’ll review immediately ahead. 2 12345678901234567890123456789012123456789012345678901 a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Additional Rules for Exponents 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To cover all your bases, also keep in mind these three additional rules for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exponents: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. When raising an exponential number to a power, multiply 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exponents: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~ax !y 5 ax y 2 12345678901234567890123456789012123456789012345678901 2 1 2 238 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Any number other than zero (0) raised to the power of 0 (zero) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equals 1: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a0 5 1 [a Þ 0] 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Raising a base number to a negative exponent is equivalent to 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 divided by the base number raised to the exponent’s absolute 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 value: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 a2x 5 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The preceding three rules are all fair game for the GM AT. In fact, a GM AT 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 question might require you to apply more than one of these rules. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~2 3 !2 3 4 23 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 16 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 26 26 2 12345678901234567890123456789012123456789012345678901 3 2 23 ~2!~3! 5 5 651 ! 3 4 5 2 3 The correct answer is D. ~2 2 12345678901234567890123456789012123456789012345678901 3 3 2 12345678901234567890123456789012123456789012345678901 4 4 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Exponents You Should Know 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the GM AT, memorize the exponential values in the following table. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You’ll be glad you did, since these are the ones you’re most likely to see on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the exam. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Power and Corresponding Value 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Base 2 3 4 5 6 7 8 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 4 8 16 32 64 128 256 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 9 27 81 243 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 16 64 256 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 25 125 625 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 36 216 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 239

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Roots and Radicals 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the flip side of exponents and powers are roots and radicals. The 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 square root of a number n is a number that you “ square” (multiply by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 itself, or raise to the power of 2), to obtain n. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 5 4 (the square root of 4) because 2 3 2 (or 2 ) 5 4 = 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The cube root of a number n is a number that you raise to the power of 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (multiply by itself twice) to obtain n. You determine greater roots (for 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 example, the “ fourth root” ) in the same way. Except for square roots, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 radical sign will indicate the root to be taken. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3 3 2 12345678901234567890123456789012123456789012345678901 2 5 8 (the cube root of 8) because 2 3 2 3 2 (or 2 ) 5 8 = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 4 2 12345678901234567890123456789012123456789012345678901 16 (the fourth root of 16) because 2 3 2 3 2 3 2 (or 2 ) 5 16 2 5 = 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the GM AT, you should know the rules for simplifying and for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combining radical expressions. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Simplifying Radicals 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, always look for the possibility of simplifying radicals by 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 moving what’s under the radical sign to the outside of the sign. Check 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 inside your square-root radicals for perfect squares: factors that are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 squares of nice tidy numbers or other terms. The same advice applies to 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 perfect cubes, and so on. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 4 and a are both perfect squares; 2 4a 5 2a 12345678901234567890123456789012123456789012345678901 = 2 12345678901234567890123456789012123456789012345678901 remove them from under the radical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sign, and find each one’s square root. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 =8a3 5 =~4!~2!a3 8 and a are both perfect cubes, which 22 12345678901234567890123456789012123456789012345678901 contain perfect-square factors; remove 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2a=2a the perfect squares from under the radi12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 cal sign, and find each one’s square root. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can simplify radical expressions containing fractions in the same way. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Just be sure that what’s in the denominator under the radical sign stays in 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the denominator when you remove it from under the radical sign. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 20x ~4!~5! 2 =5 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 3 2 2 12345678901234567890123456789012123456789012345678901 x x x 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 3 3 3 1 3 2 12345678901234567890123456789012123456789012345678901 5 5 =3 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 8 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 240 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Tip

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Whenever you see a non-prime number under a square-root radical sign, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factor it to see if it contains perfect-square factors you can move outside 2 12345678901234567890123456789012123456789012345678901 the radical sign. The same applies to cube roots and other, greater roots. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ore than likely, this step is needed to solve the problem at hand. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 4 2 12345678901234567890123456789012123456789012345678901 28a b 2345678901234567890123456789012123456789012345678901 2 1 5 2 12345678901234567890123456789012123456789012345678901 4 6 2 12345678901234567890123456789012123456789012345678901 36a b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 a A. a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 b 2b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a B. a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2b b 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a C. 2 12345678901234567890123456789012123456789012345678901 =7 2 12345678901234567890123456789012123456789012345678901 3b 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a2 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 2 = 2 2 12345678901234567890123456789012123456789012345678901 3b 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2a 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3b 2 12345678901234567890123456789012123456789012345678901 4 4 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Divide a and b from the numerator and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 denominator of the fraction. Also, factor out 4 from 28 and 36. Then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remove perfect squares from under the radical sign: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 28a6 b 4 7a2 a=7 a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 , or =7 5 5 4 6 2 2 12345678901234567890123456789012123456789012345678901 36a b 9b 3b 3b 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In GM AT questions involving radical terms, you might want to remove a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 radical term from a fraction’s denominator to match the correct answer. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To accomplish this, multiply both numerator and denominator by the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 radical value. (This process is called “ rationalizing the denominator.” ) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s an example of how to do it: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 =15 3 =15 3 =15 3 1 2 12345678901234567890123456789012123456789012345678901 5 , or =15 5 5 2 12345678901234567890123456789012123456789012345678901 15 15 5 2 12345678901234567890123456789012123456789012345678901 15 =15 =15 = 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 241

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Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Combining Radical Terms 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The rules for combining terms that include radicals are quite similar to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 those for exponents. Keep the following two rules in mind; one applies to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 addition and subtraction, while the other applies to multiplication and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 division. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 A ddition and subtraction: If a term under a radical is being added to or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subtracted from a term under a different radical, you cannot combine the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two terms under the same radical. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 1 y Þ x 1 y = = = 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 x 2 =y Þ =x 2 y = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 1 x 5 2 x , not 2x = = = = 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, if you’re asked to combine radical terms by adding or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subtracting, chances are you’ll also need to simplify radical expressions 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 along the way. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 =24 2 =16 2 =6 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. =6 2 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 4 2 2 = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 6 2 12345678901234567890123456789012123456789012345678901 = 2 12345678901234567890123456789012123456789012345678901 E. 2 =2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Although the numbers under the three radicals 2 2 12345678901234567890123456789012123456789012345678901 combine to equal 2, you cannot combine terms this way. Instead, simplify 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the first two terms, then combine the first and third terms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 =24 2 =16 2 =6 5 2 =6 2 4 2 =6 5 =6 2 4. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ultiplication and D ivision: Terms under different radicals can be 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 combined under a common radical if one term is multiplied or divided by 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the other, but only if the radical is the same. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x x 5~ x ! , or x == = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 =x =y 5 =x y 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 =x 5 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y y = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 x x 5 ? = = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 242 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 1 1 5 2 12345678901234567890123456789012123456789012345678901 3 12 3 2 3 6 2 12345678901234567890123456789012123456789012345678901 ~you cannot easily combine =x =x 5 x x 5 x 5x ! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~2 =2a!2 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 B. 4a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. 8a 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 8a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 E. 6a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Square each of the two terms, 2 and 2a, = 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 separately. Then combine their squares by multiplication: ~2 =2a!2 5 2 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 3 ~ 2a! 5 4 3 2a 5 8a. 2 = 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Roots You Should Know 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the GM AT, memorize the roots in the following table. If you encounter 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one of these radical terms on the exam, chances are you’ll need to know its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equivalent integer to answer the question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In the table on the following page, notice that positive numbers have two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 square roots, one positive and one negative. Also notice that positive 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers have only one cube root, which is a positive number; while 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 negative numbers have only one cube root, which is a negative number. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll explore further the relationship between roots and number signs if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you advance to the N ext Level. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 243

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Square roots of “perfect Cube roots of “perfect cube” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 square” integers integers (positive and negative) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!8 5 ~2!2 = 121 5 611 = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3 2 12345678901234567890123456789012123456789012345678901 ~2!27 5 ~2!3 = 144 5 612 = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2345678901234567890123456789012123456789012345678901 2 1 =~2!64 5 ~2!4 =169 5 613 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!125 5 ~2!5 = 196 5 614 = 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!216 5 ~2!6 = 225 5 615 = 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!343 5 ~2!7 = 625 5 625 = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!512 5 ~2!8 = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!729 5 ~2!9 = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 ~2!1000 5 ~2!10 = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Linear Equations in One Variable 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Algebraic expressions are usually used to form equations, which set two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 expressions equal to each other. M ost equations you’ll see on the GM AT 2 2 12345678901234567890123456789012123456789012345678901 are linear equations, in which the variables don’t come with exponents. To 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solve any linear equation containing one variable, your goal is always the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same: Isolate the unknown (variable) on one side of the equation. To 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accomplish this, you may need to perform one or more of the following 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 operations on both sides, depending on the equation: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. Add or subtract the same term from both sides 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. M ultiply or divide by the same term on both sides 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Clear fractions by cross-multiplication 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Clear radicals by raising both sides to the same power (exponent) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Performing any of these operations on both sides does not change the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equality; it merely restates the equation in a different form. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 244 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The operation you perform on one side of an equation must also be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perform on the other side; otherwise, the two sides won’t be equal! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Let’s take a look at each of these four operations to see when and how to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use each one. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Add or subtract the same term from both sides of the equation. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 To solve for x , you may need to either add or subtract a term from both 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sides of an equation—or do both. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If 2x 2 6 5 x 2 9, then x 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 29 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 26 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 23 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. First, put both x -terms on the left side of the 2 12345678901234567890123456789012123456789012345678901 equation by subtracting x from both sides; then combine x -terms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2x 2 6 2 x 5 x 2 9 2 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 6 5 29 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, isolate x by adding 6 to both sides: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 6 1 6 5 29 1 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5 23 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. M ultiply or divide both sides of the equation by the same non-zero 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 term. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To solve for x , you may need to either multiply or divide a term from both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sides of an equation. O r, you may need to multiply and divide. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 245

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 11 3 2 12345678901234567890123456789012123456789012345678901 If 12 5 2 , then x 5 2 12345678901234567890123456789012123456789012345678901 x x 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 A. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 11 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2345678901234567890123456789012123456789012345678901 2 1 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 11 2345678901234567890123456789012123456789012345678901 2 1 D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 11 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. First, combine the x -terms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 11 2 3 2 12345678901234567890123456789012123456789012345678901 12 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext, clear the fraction by multiplying both sides by x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12x 5 2 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12x 5 8 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Finally, isolate x by dividing both sides by 12: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 8 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5 , or 2 12345678901234567890123456789012123456789012345678901 12 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. If each side of the equation is a fraction, your best bet is to cross2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiply. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Where the original equation equates two fractions, use cross- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiplication to eliminate the fractions. M ultiply the numerator from one 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 side of the equation by the denominator from the other side. Set the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 product equal to the product of the other numerator and denominator. (In 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effect, cross-multiplication is a shortcut method of multiplying both sides 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the equation by both denominators.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 246 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7a a 1 1 2 12345678901234567890123456789012123456789012345678901 If, 5 , then a 5 2 12345678901234567890123456789012123456789012345678901 8 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 8 2 A. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2345678901234567890123456789012123456789012345678901 2 1 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 D. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 15 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. First, cross-multiply as we’ve described: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (3)(7a) 5 (8)(a 1 1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, combine terms (distribute 8 to both a and 1): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 21a 5 8a 1 8 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, isolate a-terms on one side by subtracting 8a from both sides; then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combine the a-terms: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 21a 2 8a 5 8a 1 8 2 8a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 13a 5 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Finally, isolate a by dividing both sides by its coefficient 13: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 13a 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 13 13 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 a5 2 12345678901234567890123456789012123456789012345678901 13 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 247

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Square both sides of the equation to eliminate radical signs. Where 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the variable is under a square-root radical sign, remove the radical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sign by squaring both sides of the equation. (Use a similar technique 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 for cube roots and other roots.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If 3 2x 5 2, then x 5 = 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 A. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 9 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 3 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 4 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. First, clear the radical sign by squaring all 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 terms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~3 2 !~=2x !2 5 2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~9!~2x ! 5 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 18x 5 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ext, isolate x by dividing both sides by 18: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 2 12345678901234567890123456789012123456789012345678901 x 5 , or 2 12345678901234567890123456789012123456789012345678901 18 9 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Linear Equations in Two Variables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What we’ve covered up to this point is pretty basic stuff. If you haven’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quite caught on, you should probably stop here and consult a basic algebra 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 workbook for more practice. O n the other hand, if you’re with us so far, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 let’s forge ahead and add another variable. H ere’s a simple example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 135y11 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 248 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uick . . . what’s the value of x ? It depends on the value of y, doesn’t it? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Similarly, the value of y depends on the value of x . Without more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information about either x or y, you’re stuck; well, not completely. You 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 can express x in terms of y, and you can express y in terms of x : 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5y22 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 y5x 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Let’s look at one more: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 4x 2 9 5 y 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solve for x in terms of y: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 4x 5 y 1 9 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 9 3 2 12345678901234567890123456789012123456789012345678901 x5 y1 2 12345678901234567890123456789012123456789012345678901 8 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Solve for y in terms of x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4x 2 9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5y 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~4x 2 9! 5 y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 x 265y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To determine numerical values of x and y, you need a system of two linear 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equations with the same two variables. Given this system, there are two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 different methods for finding the values of the two variables: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. The substitution method 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The addition-subtraction method 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ext, we’ll apply each method to determine the values of two variables in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a two-equation system. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 249

Part III: Q uantitative A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can’t solve one equation if it contains two unknowns (variables). You 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 either need to know the value of one of the variables, or you need a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 second equation. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The Substitution Method 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To solve a system of two equations using the substitution method, follow 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 these steps (we’ll use x and y here): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. In either equation, isolate one variable (x ) on one side. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. Substitute the expression that equals x in place of x in the other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Solve that equation for y. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. N ow that you know the value of y, plug it into either equation to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find the value of x . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 p 2 12345678901234567890123456789012123456789012345678901 If p 1 q 5 3q 2 10, and if q 5 10 2 p, then 5 2 12345678901234567890123456789012123456789012345678901 5 q 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 25 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 36 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Don’t let the fact that the question asks for 2 12345678901234567890123456789012123456789012345678901 q 2 12345678901234567890123456789012123456789012345678901 (rather than simply p or q) throw you. Because you’re given two linear 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equations with two unknowns, you know that you can first solve for p and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 q, then divide p by q. First thing’s first: Combine the q-terms in the first 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 5 2q 2 10 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 250 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ext, substitute (10 2 p) for q (from the second equation) in the first 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 5 2~10 2 p! 2 10 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 2 12345678901234567890123456789012123456789012345678901 p 5 20 2 2p 2 10 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 2 12345678901234567890123456789012123456789012345678901 p 5 10 2 2p 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 M ove the p-terms to the same side, then isolate p: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 1 2p 5 10 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 12 2 12345678901234567890123456789012123456789012345678901 p 5 10 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 p5 ~10! 2 12345678901234567890123456789012123456789012345678901 12 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 25 2 12345678901234567890123456789012123456789012345678901 p 5 2 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 25 12345678901234567890123456789012123456789012345678901 Substitute for p in either equation to find q (we’ll use the second 2 2 12345678901234567890123456789012123456789012345678901 2 6 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 25 2 12345678901234567890123456789012123456789012345678901 q 5 10 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 60 25 2 12345678901234567890123456789012123456789012345678901 q5 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 35 2 12345678901234567890123456789012123456789012345678901 q5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 p 2 12345678901234567890123456789012123456789012345678901 The question asks for , so do the division: 2 12345678901234567890123456789012123456789012345678901 q 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 p 6 25 2 12345678901234567890123456789012123456789012345678901 5 , or 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 q 35 35 7 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 251

SD

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The Addition-Subtraction Method 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Another way to solve for two unknowns in a system of two equations is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 with the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 addition-subtraction method. H ere are the steps: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. M ake the coefficient of either variable the same in both equations 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 (you can disregard the sign) by multiplying every term in one of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the equations. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 2. M ake sure the equations list the same variables in the same order. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Place one equation above the other. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 4. Add the two equations (work down to a sum for each term), or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subtract one equation from the other, to eliminate one variable. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. You can repeat steps 123 to solve for the other variable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 If 3x 1 4y 5 28, and if x 2 2y 5 , then x 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 212 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 B. 2 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 14 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 9 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. To solve for x , you want to eliminate y. You 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can multiply each term in the second equation by 2, then add the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 equations: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3x 1 4y 5 28 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2x 2 4y 5 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 5x 1 0y 5 27 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 x 52 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 252 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

N ote

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Since the question asked only for the value of x , stop here. If the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 had asked for both x and y (or for y only), you could have multiplied both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sides of the second equation by 3, then subtracted the second equation 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 from the first: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3x 1 4y 5 28 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 3x 2 6y 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 29 0x 1 10y 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 19 2 12345678901234567890123456789012123456789012345678901 2 10y 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 19 2 12345678901234567890123456789012123456789012345678901 y52 2 12345678901234567890123456789012123456789012345678901 20 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which Method Should You Use? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a question requires you to find values of both unknowns, you can 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 combine the two methods. For example, after using addition-subtraction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to solve for x in the last question, you can then substitute, the value of x , 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 into either equation to find y. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which method, substitution or addition-subtraction, you should use 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 depends on what the equations look like to begin with. To see what we 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mean, look again at this system: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 1 q 5 3q 2 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 q 5 10 2 p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N otice that the second equation is already set up nicely for the substitution 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 method. This system is an ideal candidate for the substitution method. You 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 could use addition-subtraction instead; however, you’d just have to 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 rearrange the terms in both the equations first: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 p 2 2q 5 210 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 p 1 q 5 10 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 253

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look again at the following system: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3x 1 4y 5 28 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 2y 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 N otice that the x -term and y-term already line up nicely here. Also, notice 2 2 12345678901234567890123456789012123456789012345678901 that it’s easy to match the coefficients of either x or y: multiply both sides 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the second equation by either 3 or 2. This system is an ideal candidate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for addition-subtraction. To appreciate this point, try using substitution 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 instead. You’ll discover that it takes far more number crunching. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To solve a system of two linear equation in two variables, use 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 addition-subtraction if you can quickly and easily eliminate one of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 variables. O therwise, use substitution. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 Linear Equations that Cannot be Solved 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ever assume that one linear equation with one variable is solvable. If you 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 can reduce the equation to 0 5 0, then you can’t solve it. In other words, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the value of the variable could be any real number. The test-makers 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 generally use the Data Sufficiency format to cover this concept. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If 3x 2 3 2 4x 5 x 2 7 2 2x 1 4, then what is the value of x ? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (1) x . 21 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) x , 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. All terms on both sides subtract out: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3x 2 3 2 4x 5 x 2 7 2 2x 1 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2x 2 3 5 2x 2 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 0 5 0 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, even considering both statements together, x could equal any real 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number between 21 and 1 (not just the integer 0). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In some cases, what appears to be a system of two equations in two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 variables might actually be the same equation expressed in two different 2 12345678901234567890123456789012123456789012345678901 2 ways. In other words, what you’re really dealing with are two equivalent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equations, which you cannot solve. The test-makers generally use the Data 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sufficiency format to cover this concept. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 254 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Does a 5 b ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (1) a 1 b 5 30 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (2) 2b 5 60 2 2a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. An unwary test-taker might assume that the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 values of both a and b can be determined with both equations together, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 because they appear at first glance to provide a system of two linear 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 equations with two unknowns. N ot so! You can easily manipulate the 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 second equation so that it is identical to the first: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2b 5 60 2 2a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2b 5 2~30 2 a! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 b 5 30 2 a 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a 1 b 5 30 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you can see, the equation 2b 5 60 2 2a is identical to the equation 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a 1 b 5 30. Thus, a and b could each be any real number. You can’t solve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one equation in two unknowns, so the correct answer must be (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Whenever you encounter a Data Sufficiency question that calls for solving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one or more linear equations, stop in your tracks before taking pencil to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 paper. Size up the equation to see whether it’s one of the two unsolvable 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 kinds you learned about here. If so, then unless you’re given more 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 information, the correct answer will be (E). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Solving Algebraic Inequalities 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can solve algebraic inequalities in the same manner as equations. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Isolate the variable on one side of the equation, factoring and eliminating 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 terms wherever possible. H owever, one important rule distinguishes 2 12345678901234567890123456789012123456789012345678901 inequalities from equations: Whenever you multiply or divide both sides of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an inequality by a negative number, you must reverse the inequality 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 symbol. Simply put: If a . b, then 2a , 2b. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 2 4x , 8 original inequality 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 24x , 24 12 subtracted from each side; inequality unchanged 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x .1 both sides divided by 24; inequality reversed 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 255

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere are some general rules for dealing with algebraic inequalities. Study 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them until they’re second nature to you, because you’ll put them to good 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use on the GM AT. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Adding or subtracting unequal quantities to (or from) equal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quantities: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a . b, then c 1 a . c 1 b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a . b, then c 2 a , c 2 b 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Adding unequal quantities to unequal quantities: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 If a . b, and if c . d, then a 1 c . b 1 d 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Comparing three unequal quantities: 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If a . b, and if b . c, then a . c 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Combining the same positive quantity with unequal quantities by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiplication or division: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If a . b, and if x . 0, then x a . x b 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a . b, and if x . 0, then . 2 12345678901234567890123456789012123456789012345678901 x x 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x x 2 12345678901234567890123456789012123456789012345678901 , If a . b, and if x . 0, then 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. Combining the same negative quantity with unequal quantities by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiplication or division: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If a . b, and if x , 0, then x a , x b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a b 2 12345678901234567890123456789012123456789012345678901 If a . b, and if x , 0, then , 2 12345678901234567890123456789012123456789012345678901 x x 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x x 2 12345678901234567890123456789012123456789012345678901 If a . b, and if x , 0, then . 2 12345678901234567890123456789012123456789012345678901 a b 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If a . b, and if c . d, then which of the following must be true? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. a 2 b . c 2 d 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. a 2 c . b 2 d 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. c 1 d , a 2 b 2 12345678901234567890123456789012123456789012345678901 D. b 1 d , a 1 c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. a 2 c , b 1 d 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 256 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Alert!

Chapter 7: M ath Review—N umber Theory and Algebra

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. Inequality questions can be a bit confusing, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can’t they? In this problem, you need to remember that if unequal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quantities (c and d) are added to unequal quantities of the same order (a 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 and b), the result is an inequality in the same order. This rule is essentially 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what answer choice (D) says. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When handling inequality problems, you might think that by simply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plugging in some sample numbers, you can zero-in on the correct answer. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Be careful! The wrong-answers might look right, depending on the values 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you use for the different variables. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 257

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This N ext Level focuses on the following advanced topics involving 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 number theory and algebra: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The impact of exponents and radicals on the magnitude and sign 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 of numbers 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Factoring quadratic expressions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Finding the roots of quadratic equations by factoring 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Finding the roots of quadratic equations by applying the quadratic 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 formula 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Factoring non-linear equations in two variables 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Algebraic expressions and problem-solving involving certain types 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of word problems 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Exponents and the Real Number Line 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Raising base numbers to powers can have surprising effects on the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 magnitude and/or sign—negative vs. positive—of the base number. You 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 need to consider four separate regions of the real-number line: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Values greater than 1 (to the right of 1 on the number line) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Values less than 21 (to the left of 21 on the number line) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Fractional values between 0 and 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Fractional values between 21 and 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The next table indicates the impact of positive-integer exponent (x ) on 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 base number (n) for each region. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 258

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 n.1 n raised to any power: n x . 1 (the greater the ex2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x ponent, the greater the value of n ) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 n , 21 n raised to even power: n x . 1 (the greater the ex2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 ponent, the greater the value of n ) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2345678901234567890123456789012123456789012345678901 2 1 n raised to odd power: n , 1 (the greater the ex2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 ponent, the lesser the value of n ) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2345678901234567890123456789012123456789012345678901 2 1 0,n,1 n raised to any power: 0 , n , n , 1 (the greater 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 the exponent, the lesser the value of n ) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 21 , n , 0 n raised to even power: 0 , n , 1 (the greater the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 x exponent, the lesser the value of n , approaching 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 0 on the number line) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 , 0 (the greater n raised to odd power: 21 , n 2 12345678901234567890123456789012123456789012345678901 x 2 12345678901234567890123456789012123456789012345678901 the exponent, the greater the value of n , ap12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 proaching 0 on the number line) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The preceding set of rules are simple enough to understand. But when you 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 apply them to a GM AT question, it can be surprisingly easy to confuse 2 2 12345678901234567890123456789012123456789012345678901 yourself, especially if the question is designed to create confusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If 21 , x , 0, which of the following must be true? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 I. x , x 2 12345678901234567890123456789012123456789012345678901 2 3 2 12345678901234567890123456789012123456789012345678901 II. x , x 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 III. x , x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. I only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. II only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. I and II only 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. I and III only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. I, II, and III 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The key to analyzing each equation is that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 raising x to successively greater powers moves the value of x closer to zero 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (0) on the number line. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (I) must be true. Since x is given as a negative number; x must be positive 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and thus greater than x . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 (II) cannot be true. Since x is given as a negative number; x must be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 positive, while x 3 must be negative. Thus, x 2 is greater than x 3 . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 (III) must be true. Both x and x are negative fractions between 0 and 21, 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 but x is closer to zero (0) on the number line—that is, greater than x . 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 259

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Roots and the Real Number Line 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As with exponents, the root of a number can bear a surprising relationship 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the mgnitude and/or sign (negative vs. positive) of the number (another 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the test-makers’ favorite areas). H ere are four rules you should 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remember: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 1. If n . 1, then 1 , =n , =n , n (the greater the root, the lesser 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the value). H owever, if n lies between 0 and 1, then 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 n , n , n , 1 = = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 (the greater the root, the greater the value). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 5 64 1 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n5 2 3 12345678901234567890123456789012123456789012345678901 64 2 12345678901234567890123456789012123456789012345678901 1 , =64 , =64 ,64 2 12345678901234567890123456789012123456789012345678901 3 1 2 12345678901234567890123456789012123456789012345678901 1 1 1 , 4 , 8 , 64 2 12345678901234567890123456789012123456789012345678901 , , ,1 2 12345678901234567890123456789012123456789012345678901 64 64 64 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 1 1 2 12345678901234567890123456789012123456789012345678901 , , ,1 2 12345678901234567890123456789012123456789012345678901 64 8 4 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Every negative number has exactly one cube root, and that root is a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 negative number. The same holds true for all other odd-numbered 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 roots of negative numbers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 3 2 12345678901234567890123456789012123456789012345678901 2 27 5 23 232 5 22 = = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (22)(22)(22)(22)(22) 5 232 (23)(23)(23) 5 227 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Every positive number has two square roots: a negative number and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a positive number (with the same absolute value). The same holds 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 true for all other even-numbered roots of positive numbers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 =16 5 64 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 81 5 63 = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Every positive number has only one cube root, and that root is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 always a positive number. The same holds true for all other 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 odd-numbered roots of positive numbers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 260 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Î Î

www.petersons.com

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The square root (or other even-number root) of any negative number is an 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 imaginary number, not a real number. That’s why the preceding rules 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t cover these roots. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Which of the following inequalities, if true, is sufficient alone to 2 12345678901234567890123456789012123456789012345678901 5 3 2 12345678901234567890123456789012123456789012345678901 x , x ? show that = = 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. 21 , x , 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 0 , x , 1 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 C. |x | , 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. |x | . 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. x , 21 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. If x , 21, then applying a greater root yields a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lesser negative value—further to the left on the real number line. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Factorable Quadratic Expressions in One 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 Variable 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A quadratic ex pression includes a “ squared” variable, such as x 2 . An 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation is quadratic if you can express it in this general form: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ax 2 1 bx 1 c 5 0, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 where: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x is the variable 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a, b, and c are constants (numbers) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 aÞ0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 b can equal 0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 c can equal 0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere are four examples (notice that the b-term and c-term are not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essential; in other words, either b or c, or both, can equal zero): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Same Equation, but in the form: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Quadratic Equation ax 2 1 bx 1 c 5 0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2w 2 5 16 2w 2 2 16 5 0 (no b-term) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 2 5 3x x 2 2 3x 5 0 (no c-term) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 3y 5 4 2 y y 1 3y 2 4 5 0 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 2z 7z 5 2z 2 15 2 7z 2 15 5 0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 261

Part III: Q uantitative A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Every quadratic equation has exactly two solutions, called roots. (But the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two roots might be the same.) O n the GM AT, you can often find the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 roots by factoring. To solve any factorable quadratic equation, follow 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 these three steps: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. Put the equation into the standard form: ax 1 bx 1 c 5 0. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2. Factor the terms on the left side of the equation into two linear 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expressions (with no exponents). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 3. Set each linear expression (root) equal to zero and solve for the 2 2 12345678901234567890123456789012123456789012345678901 2 variable in each one. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Factoring Simple Quadratic Expressions 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Some quadratic expressions are easier to factor than others. If either of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two constants b or c is zero, factoring requires no sweat. In fact, in some 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 cases, no factoring is needed at all: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A quadratic with no c term A quadratic with no b term 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2x 2 5 x 2x 2 2 4 5 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 2x 2 x 5 0 2~x 2 2! 5 0 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x ~2x 2 ! 5 0 x2 2 2 5 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 5 2 x 5 0, 2x 2 1 5 0 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 x 5 =2, 2 =2 2 12345678901234567890123456789012123456789012345678901 x 5 0, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When dealing with a quadratic equation, your first step is usually to put it 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 into the general form ax 2 1 bx 1 c 5 0. But keep in mind: The only 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essential term is ax 2 . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 262 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Factoring Quadratic Trinomials 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A trinomial is simply an algebraic expression that contains three terms. If 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a quadratic expression contains all three terms of the standard form 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ax 2 1 bx 1 c, then factoring becomes a bit trickier. You need to apply the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 FOIL method, in which you add together these terms: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 (F) the product of the first terms of the two binomials 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (O) the product of the outer terms of the two binomials 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (I) the product of the inner terms of the two binomials 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (L) the product of the last (second) terms of the two binomials 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ote the following relationships: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 (F) is the first term (ax ) of the quadratic expression 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (O 1 I) is the second term (bx ) of the quadratic expression 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (L) is the third term (c) of the quadratic expression 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You’ll find that the two factors will be two binomials. The GM AT might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ask you to recognize one or both of these binomial factors. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 x 2 6 ? Which of the following is a factor of x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. (x 1 6) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. (x 2 3) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. (x 1 1) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. (x 2 2) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. (x 1 3) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 The correct answer is B. N otice that x has no coefficient. This makes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the process of factoring into two binomials easier. Set up two binomial 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shells: (x )(x ). The product of the two missing second terms (the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ L” term under the FO IL method) is 26. The possible integral pairs that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 result in this product are (1,26), (21,6), (2,23,), and (22,3). N otice that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the second term in the trinomial is 2x . This means that the sum of the two 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 integers whose product is 26 must be 21. The pair (2,23) fits the bill. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Thus, the trinomial is equivalent to the product of the two binomials 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (x 1 2) and (x 2 3). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To check your work, multiply the two binomials using the FO IL method: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ~x 1 2!~x 2 3! 5 x 2 3x 1 2x 2 6 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 x2 2 x 1 6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 263

Part III: Q uantitative A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the preceding question had asked you to determine the roots of the 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 equation x 2 x 2 6 5 0, you’d simply set each of the binomial factors 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 equal to 0 (zero), then solve for x in each one. The solution set (the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible values of x ) includes the roots 22 and 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 H ow many different values of x does the solution set for the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 equation 4x 5 4x 2 1 contain? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. N one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. O ne 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 C. Two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Four 2 12345678901234567890123456789012123456789012345678901 E. Infinitely many 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. First, express the equation in standard form: 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 4x 2 4x 1 1 5 0. N otice that the c-term is 1. The only two integral pairs 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that result in this product are (1,1) and (2121). Since the b-term (24x ) is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 negative, the integral pair whose product is 1 must be (2121). Set up a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 binomial shell: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (? 2 1)(? 2 1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that the a-term contains the coefficient 4. The possible integral 2 2 12345678901234567890123456789012123456789012345678901 pairs that result in this product are (1,4), (2,2), (21,24), and (22,22). A 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bit of trial-and-error reveals that only the pair (2,2) works. Thus, in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 factored form, the equation becomes (2x 2 1)( 2x 2 1) 5 0 . To check your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 work, multiply the two binomials using the FO IL method: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~2x 2 1!~2x 2 1! 5 4x 2 2 2x 2 2x 1 1 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 4x 2 2 4x 1 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Since the two binomial factors are the same, the two roots of the equation 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are the same. In other words, x has only one possible value. (Although you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t need to find the value of x in order to answer the question, solve for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 .) x in the equation 2x 21 5 0; x 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 264 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Stealth Quadratic Equations 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Some equations that appear linear (variables include no exponents) may 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 actually be quadratic. Following, you will see the two GM AT situations 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you need to be on the lookout for. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1. The same variable inside a radical also appears outside: 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5 5x = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2345678901234567890123456789012123456789012345678901 2 1 ~=x ! 5 ~5x ! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 x 5 25x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 25x 2 x 5 0 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2. The same variable that appears in the denominator of a fraction 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 also appears elsewhere in the equation: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 3 2 x 2 12345678901234567890123456789012123456789012345678901 x 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 5 x ~3 2 x ! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 5 3x 2 x 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 2 3x 1 2 5 0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In both scenarios, you’re dealing with a quadratic (non-linear) equation in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 one variable. So, in either equation, there are two roots. (Both equations 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 are factorable, so go ahead and find their roots.) The test-makers often use 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the Data Sufficiency format to cover this concept. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 What is the value of x ? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (1) 6x 5 =3x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (2) x . 0 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. An unwary test-taker might assume that the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 equation in statement (1) is linear—because x is not squared. N ot so! Clear 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the radical by squaring both sides of the equation, then isolate the x -terms 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 on one side of the equation and you’ll see that the equation is quite 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quadratic indeed: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 36x 2 5 3x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 36x 2 3x 5 0 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 265

Part III: Q uantitative A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 To ferret out the two roots, factor out 3x , then solve for each root: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3x ~12x 2 1! 5 0 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3x 5 0; 12x 2 1 50 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 x 5 0, 2345678901234567890123456789012123456789012345678901 2 1 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Since there is more than one possible value for x , statement (1) alone is 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 insufficient to answer the question. Statement (2) alone is obviously 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 insufficient. But the two together eliminate the root value 0, leaving as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12 2 12345678901234567890123456789012123456789012345678901 the only possible value of x . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The Quadratic Formula 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For some quadratic equations, although rational roots exist, they’re 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 x 2 6 5 0 can be solved by difficult to find. For example, 12x 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 factoring, but the factors are not easy to see: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12x 2 1 x 2 6 5 (3x 2 2)(4x 1 3) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Faced with a quadratic equation that’s difficult to factor, you can always 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 use the quadratic formula, which states that, for any equation of the form 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ax 2 1 bx 1 c 5 0: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 b 2 4ac 2b 6 = 2 12345678901234567890123456789012123456789012345678901 x 5 2 12345678901234567890123456789012123456789012345678901 2a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 x 2 6 5 0, for example, a 5 12, b 5 1, and c 5 2 6. In the equation 12x 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Plugging these value into the quadratic formula, you’ll find that the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 3 2 12345678901234567890123456789012123456789012345678901 roots are and 2 . 2 12345678901234567890123456789012123456789012345678901 3 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Some quadratic equations have no rational roots (solutions). Referring to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 the quadratic formula, if =b 2 4ac turns out to be a negative number, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then its square root will be im aginary, and hence so will the roots of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 quadratic equation at hand. But, the GM AT doesn’t test you on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 imaginary numbers. In other words, you’ll find only real-number 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (rational) roots of any GM AT quadratic equation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 266 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Non-Linear Equations in Two Variables 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the world of math, solving non-linear equations in two or more 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 variables can be very complicated, even for bona-fide mathematicians. But 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the GM AT, all you need to remember are these three general forms: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 12345678901234567890123456789012123456789012345678901 Sum of two variables, squared: (x 1 y) 5 x 1 2x y 1 y 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 12345678901234567890123456789012123456789012345678901 Difference of two variables, squared: (x 2 y) 5 x 2 2x y 1 y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 Difference of two squares: x 2 y 5 (x 1 y)(x 2 y) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can verify these equations using the FO IL method: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (x 1 y)2 (x 2 y)2 (x 1 y)(x 2 y) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 5 (x 1 y)(x 1 y) 5 (x 2 y)(x 2 y) 1 x y 2 x y 2 y 5 x 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 2 2 2 2 2 2 12345678901234567890123456789012123456789012345678901 5x 2y 5 x 1 xy 1 xy 1 y 5 x 2 xy 2 xy 1 y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 5 x 1 2x y 1 y 5 x 2 2x y 1 y 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the GM AT, memorize the three equations listed here. When you see 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 one form on the exam, it’s a sure bet that your task is to rewrite it as the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other form. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If x 2 2 y 2 5 100, and if x 1 y 5 2, then x 2 y 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 22 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 10 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 20 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 50 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 200 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. If you’re on the lookout for the difference of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two squares, you can handle this question with no sweat. Use the third 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation you just learned, substituting 2 for (x 1 y), then solving for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (x 2 y): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 x 2 y 5 (x 1 y)(x 2 y) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 100 5 ~x 1 y!~x 2 y! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 100 5 ~2!~x 2 y! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 50 5 ~x 2 y! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 267

Part III: Q uantitative A bility

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Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What about working backward from the answer choices to solve this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem? Go ahead and try it. You don’t get very far, do you? There are 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 two lessons here: (1) You usually can’t solve quadratics using a shortcut, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and (2) always look for one of the three common quadratic forms; if you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 see it, rewrite it as its equivalent form to answer the question as quickly 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 and easily as possible. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Weighted Average Problems 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 You solve w eighted average problems using the arithmetic mean (simple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average) formula, except you give the set’s terms different weights. For 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 example, if a final exam score of 90 receives tw ice the weight of each of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two mid-term exam scores 75 and 85, think of the final-exam score as tw o 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 scores of 90—and the total number of scores as 4 rather than 3: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 75 1 85 1 ~2!~90! 340 2 12345678901234567890123456789012123456789012345678901 WA 5 5 5 85 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Similarly, when some numbers among terms might appear more often than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 others, you must give them the appropriate “ weight” before computing an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 During an 8-hour trip, Brigitte drove 3 hours at 55 miles per hour 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and 5 hours at 65 miles per hour. What was her average rate, in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 miles per hour, for the entire trip? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 A. 58.5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 60 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 61.25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 62.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 66.25 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Determine the total miles driven: (3)(55) 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (5)(65) 5 490. To determine the average over the entire trip, divide this 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 total by 8, which is the number of total hours: 490 4 8 5 61.25. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A tougher weighted-average problem might provide the weighted average 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and ask for one of the terms, or require conversions from one unit of 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 measurement to another—or both. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 268 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A certain olive orchard produces 315 gallons of oil annually, on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 average, during four consecutive years. H ow many gallons of oil 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must the orchard produce annually, on average, during the next six 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 years, if oil production for the entire 10-year period is to meet a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 goal of 378 gallons per year? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A. 240 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 285 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 396 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. 420 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 468 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 The correct answer is D. In the weighted-average formula, 315 annual 2 2 12345678901234567890123456789012123456789012345678901 gallons receives a weight of 4, while the average annual number of gallons 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for the next six years (x ) receives a weight of 6: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1,260 1 6x 2 12345678901234567890123456789012123456789012345678901 378 5 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3,780 5 1,260 1 6x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3,780 2 1,260 5 6x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 420 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 This solution (420) is the average number of gallons needed per year, on 12345678901234567890123456789012123456789012345678901 22 average, during next 6 years. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To guard against calculation errors, check your answer by sizing up the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. Generally, how great a number are you looking for? N otice that 2 12345678901234567890123456789012123456789012345678901 the stated goal is a bit greater than the annual average production over the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first four years. So you’re looking for an answer that is greater than the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 goal — a number somewhat greater than 378 gallons per year. You can 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 eliminate choice (A) and (B) out of hand. The number 420 fits the bill. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Currency (Coin and Bill) Problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Currency problems are similar to weighted-average problems in that each 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 item (bill or coin) is weighted according to its monetary value. Unlike 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 weighted average problems, however, the “ average” value of all the bills 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 or coins is not at issue. In solving currency problems, remember the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • You must formulate algebraic expressions involving both num ber 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of items (bills or coins) and value of items. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 269

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • You should convert the value of all moneys to a common currency 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unit before formulating an equation. If converting to cents, for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example, you must multiply the number of nickels by 5, dimes by 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 10, and so forth. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Jim has $2.05 in dimes and quarters. If he has four fewer dimes 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 than quarters, how much money does he have in dimes? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 20 cents 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. 30 cents 2 12345678901234567890123456789012123456789012345678901 2 C. 40 cents 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 50 cents 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. 60 cents 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. Letting x equal the number of dimes, x 1 4 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 represents the number of quarters. The total value of the dimes (in cents) is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10x , and the total value of the quarters (in cents) is 25(x 1 4) or 25x 1 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 100. Given that Jim has $2.05, the following equation emerges: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 10x 1 25x 1 100 5 205 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 35x 5 105 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 53 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Jim has three dimes, so he has 30 cents in dimes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You could also solve this problem without formal algebra, by plugging in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each answer choice in turn. Let’s try this strategy for choices (A) and (B): 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 20 cents is 2 dimes, so Jim has 6 quarters. 20 cents plus $1.50 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adds up to $1.70. Wrong answer! 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 30 cents is 3 dimes, so Jim has 7 quarters. 30 cents plus $1.75 2 12345678901234567890123456789012123456789012345678901 2 adds up to $2.05. Correct answer! 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can also solve most GM AT currency problems by working backward 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from the answer choices. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 270 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Mixture Problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In GM AT mixture problems, you combine substances with different 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 characteristics, resulting in a particular mixture or proportion, usually 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expressed as percentages. Substances are measured and mixed by either 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 volume or weight — rather than by number (quantity). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow many quarts of pure alcohol must you add to 15 quarts of a 2 12345678901234567890123456789012123456789012345678901 solution that is 40% alcohol to strengthen it to a solution that is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 50% alcohol? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4.0 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 3.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 3.25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 3.0 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 2.5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. You can solve this problem by working 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 backward from the answer choices—trying out each one in turn. O r, you 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 can solve the problem algebraically. The original amount of alcohol is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 40% of 15. Letting x equal the number of quarts of alcohol that you must 2 2 12345678901234567890123456789012123456789012345678901 add to achieve a 50% alcohol solution, .4(15) 1 x equals the amount of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alcohol in the solution after adding more alcohol. You can express this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 amount as 50% of (15 1 x ). Thus, you can express the mixture 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 algebraically as follows: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~.4!~15! 1 x 5 ~.5!~15 1 x ! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 1 x 5 7.5 1 .5x 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 .5x 5 1.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You must add 3 quarts of alcohol to obtain a 50% alcohol solution. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Investment Problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT investment problems involve interest earned (at a certain 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 percentage rate) on money over a certain time period (usually a year). To 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 calculate interest earned, multiply the original amount of money by the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interest rate: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 amount of money 3 interest rate 5 amount of interest on money 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For example, if you deposit $1,000 in a savings account that earns 5% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interest annually, the total amount in the account after one year will be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 $1,000 1 .05($1,000) 5 $1,000 1 $50 5 $1,050. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 271

Part III: Q uantitative A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 GM AT investment questions usually involve more than simply calculating 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interest earned on a given principal amount at a given rate. They usually 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 call for you to set up and solve an algebraic equation. When handling these 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 problems, it’s best to eliminate percent signs. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dr. Kramer plans to invest $20,000 in an account paying 6% 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 interest annually. H ow much more must she invest at the same time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 at 3% so that her total annual income during the first year is 4% of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 her entire investment? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 A. $32,000 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. $36,000 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. $40,000 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. $47,000 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. $49,000 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Letting x equal the amount invested at 3% , 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you can express Dr. Kramer’s total investment as 20,000 1 x . The interest 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on $20,000 plus the interest on the additional investment equals the total 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interest from both investments. You can state this algebraically as follows: 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 .06(20,000) 1 .03x 5 .04(20,000 1 x ) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ultiply all terms by 100 to eliminate decimals, then solve for x : 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 6~20,000! 1 3x 5 4~20,000 1 x ! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 120,000 1 3x 5 80,000 1 4x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 40,000 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 She must invest $40,000 at 3% for her total annual income to be 4% of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 her total investment ($60,000). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In solving GM AT investment problems, by all means size up the question 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to make sure your calculated answer is in the right ballpark. But don’t rely 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on your intuition to derive a precise solution. Interest problems can be 2 2 12345678901234567890123456789012123456789012345678901 misleading. For instance, you might have guessed that Dr. Kramer would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to invest more than tw ice as much at 3% than at 6% to lower the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 overall interest rate to 4% . N ot true! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 272 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Problems Involving Rate of Production 2 12345678901234567890123456789012123456789012345678901 2 or112345678901234567890123456789012123456789012345678901 Work 2345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A rate is a fraction that expresses a quantity per unit of time. For example, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rate at which a machine produces a certain product is expressed this way: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 number of units produced 2 12345678901234567890123456789012123456789012345678901 rate of production 5 2 12345678901234567890123456789012123456789012345678901 time 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 A simple GM AT rate question might simply provide two of the three 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terms, and then ask you for the value of the third term. To complicate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 matters, the question might also require you to convert a number from one 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 unit of measurement to another. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A printer can print pages at a rate of 15 pages per minute, how 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 many pages can it print in 2 hours? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 1,375 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 1,500 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 1,750 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 2,250 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 2,500 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. Apply the following formula: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 no. of pages 2 12345678901234567890123456789012123456789012345678901 rate 5 2 12345678901234567890123456789012123456789012345678901 time 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The rate is given as 15 minutes, so convert the time (2 hours) to 150 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 minutes. Determine the number of pages by applying the formula to these 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 no. of pages 2 12345678901234567890123456789012123456789012345678901 15 5 2 12345678901234567890123456789012123456789012345678901 150 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~15!~150! 5 no. of pages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2,250 5 no. of pages 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A more challenging type of rate-of-production (work) problem involves 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 two or more workers (people or machines) working together to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 accomplish a task or job. In these scenarios, there’s an inverse relationship 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 between the number of workers and the time that it takes to complete the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 job; in other words, the more workers, the quicker the job gets done. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 273

Part III: Q uantitative A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A GM AT work problem might specify the rates at which certain workers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 work alone and ask you to determine the rate at which they work together, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or vice versa. H ere’s the basic formula for solving a work problem: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A A 2 12345678901234567890123456789012123456789012345678901 1 5 1 2 12345678901234567890123456789012123456789012345678901 x y 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this formula: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • x and y represent the time needed for each of two workers, x and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y, to complete the job alone. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A represents the time it takes for both x and y to complete the job 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 working in the aggregate (together). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So each fraction represents the portion of the job completed by a worker. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The sum of the two fractions must be 1 if the job is completed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the real world, teamwork often creates a synergy whereby the team is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more efficient than the individuals working alone. But on the GM AT, you 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can assume that no additional efficiency is gained by two or more workers 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 working together. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O ne printing press can print a daily newspaper in 12 hours, while 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another press can print it in 18 hours. H ow long will the job take if 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 both presses work simultaneously? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 7 hours, 12 minutes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 9 hours, 30 minutes 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 10 hours, 45 minutes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 15 hours 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 30 hours 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 274 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Just plug the two numbers 12 and 18 into our 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 work formula, then solve for A : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A A 2 12345678901234567890123456789012123456789012345678901 1 5 1 2 12345678901234567890123456789012123456789012345678901 12 18 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 3A 2A 2 12345678901234567890123456789012123456789012345678901 1 5 1 2 12345678901234567890123456789012123456789012345678901 36 36 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 5A 2 12345678901234567890123456789012123456789012345678901 51 2 12345678901234567890123456789012123456789012345678901 36 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 5A 5 36 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 36 1 2 12345678901234567890123456789012123456789012345678901 A 5 , or 7 . 2 12345678901234567890123456789012123456789012345678901 5 5 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 Both presses working simultaneously can do the job in 7 hours—or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 7 hours, 12 minutes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ad you needed to guess the answer, you could have easily ruled out 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices (D) and (E), which both nonsensically suggest that the aggregate 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 time it takes both presses together to produce the newspaper is longer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than the time it takes either press alone. Remember: In work problems, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 use your common sense to narrow down answer choices! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problems Involving Rate of Travel (Speed) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 GM AT rate problems often involve rate of travel (speed). You can express 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a rate of travel this way: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distance 2 12345678901234567890123456789012123456789012345678901 rate of travel 5 2 12345678901234567890123456789012123456789012345678901 time 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 An easier speed problem will involve a single distance, rate, and time. A 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tougher speed problem might involve different rates, such as: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Two different times over the same distance 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Two different distances covered in the same time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In either type, apply the basic rate-of-travel formula to each of the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 events. Then solve for the missing information by algebraic substitution. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Use essentially the same approach for any of the following scenarios: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • O ne object making two separate “ legs” of a trip — either in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same direction or as a round trip 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 275

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Two objects moving in the same direction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Two objects moving in opposite directions 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Janice left her home at 11 a.m., traveling along Route 1 at 30 mph. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 At 1 p.m., her brother Richard left home and started after her on 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the same road at 45 mph. At what time did Richard catch up to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Janice? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 2:45 p.m. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. 3:00 p.m. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 3:30 p.m. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 D. 4:15 p.m. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 5:00 p.m. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is E. N otice that the distance Janice covered is equal 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to that of Richard—that is, distance is constant. Letting x equal Janice’s 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time, you can express Richard’s time as x 2 2. Substitute these values for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time and the values for rate given in the problem into the speed formula for 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Richard and Janice: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Formula: rate 3 time 5 distance 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Janice: (30)(x ) 5 30x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Richard: (45)(x 2 2) 5 45x 2 90 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Because the distance is constant, you can equate Janice’s distance to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Richard’s, then solve for x : 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 30x 5 45x 2 90 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 15x 5 90 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 5 6 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Janice had traveled six hours when Richard caught up with her. Because 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Janice left at 11:00 a.m., Richard caught up with her at 5:00 p.m. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ow far in kilometers can Scott drive into the country if he drives 2 12345678901234567890123456789012123456789012345678901 out at 40 kilometers per hour (kph), returns over the same road at 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 30 kph, and spends eight hours away from home, including a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one-hour stop for lunch? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 105 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 120 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 145 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 180 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 210 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 276 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 7: M ath Review—N umber Theory and Algebra

Take It to the Next Level

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. Scott’s actual driving time is 7 hours, which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you must divide into two parts: his time spent driving into the country and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 his time spent returning. Letting the first part equal x , the return time is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 what remains of the seven hours, or 7 2 x . Substitute these expressions 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 into the motion formula for each of the two parts of Scott’s journey: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Formula: rate 3 time 5 distance 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Going: (40)(x ) 5 40x 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Returning: (30)(7 2 x ) 5 210 2 30x 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Because the journey is round trip, the distance going equals the distance 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 returning. Simply equate the two algebraic expressions, then solve for x : 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 40x 5 210 2 30x 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 70x 5 210 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 53 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Scott traveled 40 mph for 3 hours, so he traveled 120 miles. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Regardless of which type of speed problem you’re dealing with, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 should always start with the same task: set up tw o distinct equations 12345678901234567890123456789012123456789012345678901 22 patterned after the simple rate-of-travel formula (r 3 t 5 d). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problems Involving Overlapping Sets 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O verlapping set problems involve distinct sets that share some number of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 members. GM AT overlapping set problems come in one of two varieties: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Single overlap (easier) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Double overlap (tougher) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Each of the 24 people auditioning for a community-theater produc2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion is either an actor, a musician, or both. If 10 of the people 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 auditioning are actors and 19 of the people auditioning are musi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cians, how many of the people auditioning are musicians but not 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 actors? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 14 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 19 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 24 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 277

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. You can approach this relatively simple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem without formal algebra: The number of actors plus the number of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 musicians equals 29 (10 1 19 5 29). H owever, only 24 people are 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 auditioning. Thus, 5 of the 24 are actor-musicians, so 14 of the 19 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 musicians must not be actors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 You can also solve this problem algebraically. The question describes three 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mutually exclusive sets: (1) actors who are not musicians, (2) musicians 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 who are not actors, and (3) actors who are also musicians. The total 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 number of people among these three sets is 24. You can represent this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scenario with the following algebraic equation (n 5 number of actors/ 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 musicians), solving for 19 2 n to answer the question: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~10 2 n! 1 n 1 ~19 2 n! 5 24 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 29 2 n 5 24 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 n 5 5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 19 2 5 5 14 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Adrian owns 60 neckties, each of which is either 100% silk or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 100% polyester. Forty percent of each type of tie is striped, and 25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the ties are silk. H ow many of the ties are polyester but not 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 striped? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 21 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 24 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 35 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 40 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. This double-overlap problem involves four 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinct sets: striped silk ties, striped polyester ties, non-striped silk ties, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and non-striped polyester ties. Set up a table representing the four sets, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 filling in the information given in the problem, as shown in the next figure: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 silk polyester 2 12345678901234567890123456789012123456789012345678901 striped 40% 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 non-striped ? 60% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 25 35 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Given that 25 ties are silk (see the left column), 35 ties must be polyester 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (see the right column). Also, given that 40% of the ties are striped (see the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 top row), 60% must be non-striped (see the bottom row). Thus, 60% of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 35 ties, or 21 ties, are polyester and “ non-striped.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 278 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter

8 Math Review—Geometry 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this chapter, you’ll review the fundamentals involving plane geometry, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 starting with the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Relationships among angles formed by intersecting lines 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Characteristics of any triangle 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Characteristics of special right triangles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The Pythagorean theorem 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Characteristics of squares, rectangles, and parallelograms 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Characteristics of circles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Then, you’ll review the basics of coordinate geometry: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The characteristics of the x y-plane 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Defining and plotting points and lines on the plane 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Applying the midpoint and distance formulas to problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving line segments 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lines and Angles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lines and line segments are the basic building blocks for most GM AT 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 geometry problems. A GM AT geometry question might involve nothing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 more than intersecting lines and the angles they form. To handle the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question, just remember four basic rules about angles formed by 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 intersecting lines: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Vertical angles (angles across the vertex from each other and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 formed by the same two lines) are equal in degree measure, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 congruent (≅). In other words, they’re the same size. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 279

Part III: Q uantitative A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. If adjacent angles combine to form a straight line, their degree 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measures total 180. In fact, a straight line is actually a 180° angle. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. If two lines are perpendicular (⊥) to each other, they intersect, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forming right (90°) angles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. The sum of the measures of all angles where two or more lines 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 intersect at the same point is 360° (regardless of how many angles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are involved). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The symbol (≅) symbolizes that two geometric features are congruent, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which means that they are identical (the same size, length, degree 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A B ≅ CD means that line segment A B is measure, etc.). The equation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CD . The two equations congruent (equal in length) to line segment 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ∠A ≅ ∠B and m ∠A 5 m ∠B are two different ways of symbolizing the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same relationship: that the angle whose vertex is at point A is congruent 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (equal in degree measure, or size) to the angle whose vertex is at point B. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (The letter m symbolizes degree measure.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Angles Formed by Intersecting Lines 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When two or more lines intersect at the same point, they form a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ wheel-spoke” pattern with a “ hub.” O n the GM AT, “ wheel-spoke” 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions require you to apply one or more of the preceding four rules. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 y˚ 40˚ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x˚ 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The figure above shows three intersecting lines. What is the value of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 1y? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 50 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 80 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 130 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 140 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 150 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 280 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The angle vertical to the one indicated as 40° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must also measure 40°. That 40° angle, together with the angles whose 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measures are x ° and y°, combine to form a straight (180°) line. In other 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 words, 40 1 x 1 y 5 180. Thus, x 1 y 5 140. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A slightly tougher “ wheel-spoke” question might focus on overlapping 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 angles and require you to apply rule 1 (about vertical angles) to determine 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the amount of the overlap. Look at this next “ wheel-spoke” figure: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question about the preceding figure might test your ability to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recognize one of the following relationships: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x 1 y 2 z 5 180 x 1 y exceeds 180 by the amount 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the overlap, which equals z, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the angle vertical to the overlap12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ping angle. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 1 y 1 v 1 w 5 360 The sum of the measures of all 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 angles, excluding z, is 360°; z is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 excluded because it is already 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accounted for by the overlap of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x and y. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 y2w 5z w equals its vertical angle, so 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y 2 w equals the portion of y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 vertical to angle z. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 281

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Parallel Lines and Transversals 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT problems involving parallel lines also involve at least one 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 transversal, which is a line that intersects each of two (or more) lines. Look 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 at this next figure, in which l1 i l2 and l3 i l4 : 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The upper-left “ cluster” of angles 1, 2, 3, and 4 matches each of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 three other clusters. In other words: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 All the odd-numbered angles are congruent (equal in size) to one 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 All the even-numbered angles are congruent (equal in size) to one 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If you know the size of just one angle, you can determine the size of all 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 angles! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the figure above, lines P and Q are parallel to each other. If 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m∠x 5 75°, what is the measure of ∠y ? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 75° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 85° 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 95° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 105° 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 115° 2 12345678901234567890123456789012123456789012345678901 2 1 2 282 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The angle “ cluster” where lines P and R 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 intersect corresponds to the cluster where lines Q and R intersect. Thus, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ∠x and ∠y are supplementary (their measures add up to 180°). Given that 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 ∠x measures 75°, ∠y must measure 105°. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Triangles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The triangle (a three-sided polygon) is the test-makers’ favorite geometric 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 figure. You’ll need to understand triangles not only to solve “ pure” 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle problems but also to solve certain problems involving four-sided 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 figures, three-dimensional figures, and even circles. After a brief review of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the properties of any triangle, you’ll focus on right triangles (which include 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one right, or 90°, angle). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Properties of All Triangles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere are four properties that all triangles share: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. L ength of the sides. Each side is shorter than the sum of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 lengths of the other two sides. (O therwise, the triangle would 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 collapse into a line.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. A ngle m easures. The measures of the three angles total 180°. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. A ngles and opposite sides. Comparative angle sizes correspond to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the comparative lengths of the sides opposite those angles. For 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 example, a triangle’s largest angle is opposite its longest side. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (The sides opposite two congruent angles are also congruent.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t take this rule too far! The ratio among angle sizes need not be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 identical to the ratio among lengths of sides! For example, if a certain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle has angle measures of 30°, 60°, and 90°, the ratio of the angles is 2 12345678901234567890123456789012123456789012345678901 1:2:3. But this does not mean that the ratio of the opposite sides is also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1:2:3? N o, it doesn’t, as you’ll soon learn. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. A rea. The area of any triangle is equal to one-half the product of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 its base and its height (or “ altitude” ): Area 5 3 base 3 height. 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 You can use any side as the base to calculate area. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 283

Part III: Q uantitative A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Do not equate altitude (height) with any particular side. Instead, imagine 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the base on flat ground, and drop a plumb line straight down from the top 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 peak of the triangle to define height or altitude. The only type of triangle 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in which the altitude equals the length of one side is the right triangle. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Right Triangles and the Pythagorean Theorem 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 In a right triangle, one angle measures 90° (and, of course, each of the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other two angles measures less than 90°). The Pythagorean theorem 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 expresses the relationship among the sides of any right triangle. In the 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 following expression of the Theorem, a and b are the two legs (the two 2 2 12345678901234567890123456789012123456789012345678901 shortest sides) that form the right angle, and c is the hypotenuse—the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 longest side, opposite the right angle: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 a 1 b 5 c 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 For any right triangle, if you know the length of two sides, you can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine the length of the third side by applying the Theorem. For 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the two shortest sides (the legs) of a right triangle are 2 and 3 units long, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then the length of the triangle’s third side (the hypotenuse) is 13 units: = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 1 3 2 5 ~=13!2 ; 13 5 c2 ; c 5 =13 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a right triangle’s longest side (hypotenuse) is 10 units long and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another side (one of the legs) is 5 units long, then the third side is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 =3 units long: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a2 1 5 2 5 10 2 ; a2 5 75; a 5 =75 5 =~25!~3! 5 5 =3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Pythagorean Triplets 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A Pythagorean triplet is a specific ratio among the sides of a triangle that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 satisfies the Pythagorean theorem. In each of the following triplets, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first two numbers represent the comparative lengths of the two legs, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 whereas the third—and greatest—number represents the comparative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 284 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Tip

Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 length of the hypotenuse (on the GM AT, the first four appear far more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 frequently than the last two): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 12345678901234567890123456789012123456789012345678901 2! 1 1 5 ~ 1 = 1:1:=2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 1 1 ~ 3! 5 2 = 2 12345678901234567890123456789012123456789012345678901 1: 3:2 = 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 2 12345678901234567890123456789012123456789012345678901 1 4 5 5 3 3:4:5 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 12345678901234567890123456789012123456789012345678901 5 1 12 5 13 5:12:13 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 8 1 15 5 17 2 12345678901234567890123456789012123456789012345678901 8:15:17 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 12345678901234567890123456789012123456789012345678901 7 1 24 5 25 7:24:25 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each triplet above is expressed as a ratio because it represents a proportion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among the triangle’s sides. All right triangles with sides having the same 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 proportion, or ratio, have the same shape. For example, a right triangle 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with sides of 5, 12, and 13 is smaller but exactly the same shape 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (proportion) as a triangle with sides of 15, 36, and 39. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Two boats leave the same dock at the same time, one traveling due 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 east at 10 miles per hour and the other due north at 24 miles per 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hour. H ow many miles apart are the boats after three hours? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 68 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 72 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 88 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 98 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 110 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The distance between the two boats after three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hours forms the hypotenuse of a triangle in which the legs are the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 boats’ respective paths. The ratio of one leg to the other is 10:24, or 5:12. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 So you know you’re dealing with a 5:12:13 triangle. The slower boat 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 traveled 30 miles (10 mph 3 3 hours). Thirty corresponds to the number 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in the 5:12:13 ratio, so the multiple is 6 (5 3 6 5 30). 5:12:13 5 30:72:98. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To save valuable time on GM AT right-triangle problems, learn to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recognize given numbers (lengths of triangle sides) as multiples of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Pythagorean triplets. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 285

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Pythagorean Angle Triplets 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In two (and only two) of the unique triangles identified in the preceding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 section as Pythagorean side triplets, all degree measures are integers: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 1. The corresponding angles opposite the sides of a 1:1 =2 triangle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are 45°, 45°, and 90°. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 2. The corresponding angles opposite the sides of a 1:=3:2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 triangle are 30°, 60°, and 90°. 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you know that the triangle is a right triangle (one angle measures 90°) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and that one of the other angles is 45°, then given the length of any side, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you can determine the unknown lengths. For example: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If one leg is 5 units long, then the other leg must also be 5 units 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 long, while the hypotenuse must be 5 2 units long. = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If the hypotenuse (the longest side) is 10 units long, then each leg 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 units long. Divide hypotenuse by 2: must be 5 = = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 10 =2 10 2 12345678901234567890123456789012123456789012345678901 5 5 5 2 = 2 12345678901234567890123456789012123456789012345678901 2 2 = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Similarly, if you know that the triangle is a right triangle (one angle 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measures 90°) and that one of the other angles is either 30° or 60°, then 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 given the length of any side you can determine the unknown lengths. For 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If the shortest leg (opposite the 30° angle) is 3 units long, then the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other leg (opposite the 60° angle) must be 3 3 units long, and = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the hypotenuse must be 6 units long (3 3 2). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • If the longer leg (opposite the 60° angle) is 4 units long, then the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 3 = 2 12345678901234567890123456789012123456789012345678901 units long shorter leg (opposite the 30° angle) must be 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 286 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 =3 4 2 12345678901234567890123456789012123456789012345678901 ), while the hypotenuse must be 5 (divide by 3: = 2 12345678901234567890123456789012123456789012345678901 3 3 = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8 3 = 2345678901234567890123456789012123456789012345678901 2 1 (twice as long as the shorter leg). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If the hypotenuse is 10 units long, then the shorter leg (opposite 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the 30° angle) must be 5 units long, while the longer leg (opposite 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the 60° angle) must be 5 3 units long (the length of the shorter = 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 leg multiplied by =3). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A C is 8 units long, m ∠A BD 5 45°, and In the figure below, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m ∠D A C 5 60°. H ow many units long is BD ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 60˚ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 45˚ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C B D 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. 2 =2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 3 =3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 E. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. To find the length of BD , you first need to find 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A D . N otice that DA D C is a 30°-60°- 90° triangle. The ratio among its 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 sides is 1:=3:2. Given that A C is 5 units long, A D must be units long. 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 (The ratio 1:2 is equivalent to the ratio :5. N ext, notice that DA BD is a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 45°-45°-90° triangle. The ratio among its sides is 1:1:=2. You know that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 A D is BD must also be units long. Thus, units long. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 287

Part III: Q uantitative A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A 45°-45°-90° triangle is special type of isosceles triangle—a triangle with 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two congruent sides. If you advance, you’ll look more closely at this type 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of triangle, as well as at another special type: the equilateral triangle (a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle whose three sides are all congruent). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Rectangles, Squares, and Parallelograms 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Rectangles, squares, and parallelograms are types of quadrilaterals—four- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sided geometric figures. H ere are the characteristics that apply to all 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rectangles, squares, and parallelograms: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The sum of the measures of all four interior angles is 360°. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O pposite sides are parallel. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O pposite sides are congruent (equal in length). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O pposite angles are congruent (the same size, or equal in degree 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measure). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Adjacent angles are supplementary (their measures total 180°). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A rectangle is a special type of parallelogram in which all four angles are 2 2 12345678901234567890123456789012123456789012345678901 right angles (90°). A square is a special type of rectangle in which all four 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sides are congruent (equal in length). For the GM AT, you should know 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 how to determine the perimeter and area of each of these three types of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quadrilaterals. Referring to the next three figures, here are the formulas 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (l 5 length and w 5 width): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Rectangle 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Perimeter 5 2l 1 2w 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Area 5 l 3 w 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 288 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Square 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Perimeter 5 4s [s 5 side] 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 Area 5 s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 2345678901234567890123456789012123456789012345678901 2 1 (diagonal) Area 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Parallelogram 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Perimeter 5 2l 1 2w 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Area 5 base (b) 3 altitude (a) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions involving squares come in many varieties. For example, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you might need to determine area, given the length of any side or either 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 diagonal, or perimeter. O r, you might need to do just the opposite—find a 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 length or perimeter given the area. For example: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The area of a square with a perimeter of 8 is 4. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (s 5 8 4 4 5 2; s2 5 4) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The perimeter of a square with an area of 8 is. 8 =2. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (s 5 =8 5 2=2; 4s 5 4 3 2 =2) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 289

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The area of a square with a diagonal of 6 is 18. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 5 ~36! 5 6) (A 5 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O r, you might need to determine a change in area resulting from a change 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in perimeter (or vice versa). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a square’s sides are each increased by 50% , by what percent does 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 the square’s area increase? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 75% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 100% 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. 125% 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 150% 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 200% 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. Letting s 5 the length of each side before the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 2 increase, area 5 s . Let s5 the length of each side after the increase, the 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 9 9 5 3 2 12345678901234567890123456789012123456789012345678901 new area 5 s 5 s2 . The increase from s2 to s2 to is , or 125% . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 4 4 4 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions involving non-square rectangles also come in many 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible flavors. For example, a question might ask you to determine area 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 based on perimeter, or vice versa. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The length of a rectangle with area 12 is three times the rectangle’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 width. What is the perimeter of the rectangle? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 12 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 14 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 16 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 20 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The ratio of length to width is 3:1. The ratio 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 6:2 is equivalent, and 6 3 2 5 12 (the area). Thus, the perimeter 5 (2)(6) 2 2 12345678901234567890123456789012123456789012345678901 1 (2)(2) 5 16. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O r, a question might require you to determine a combined perimeter or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 area of adjoining rectangles. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 290 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the figure above, all intersecting line segments are perpendicular. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 What is the area of the shaded region, in square units? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 84 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. 118 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 128 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 139 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 238 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The figure provides the perimeters you need to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 calculate the area. O ne way to find the area of the shaded region is to 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 consider it as what remains when a rectangular shape is cut out of a larger 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 rectangle. The area of the entire figure without the “ cut-out” is 14 3 17 5 2 2 12345678901234567890123456789012123456789012345678901 238. The “ cut-out” rectangle has a length of 11, and its width is equal to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 17 2 4 2 3 5 10. Thus, the area of the cut-out is 11 3 10 5 110. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Accordingly, the area of the shaded region is 238 110 5 128. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Another way to solve the problem is to partition the shaded region into 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 three smaller rectangles, as shown in the next figure, and sum up the area 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of each. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question about a non-rectangular parallelogram might focus on 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 angle measures. These questions are easy to answer. In any parallelogram, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 opposite angles are congruent, and adjacent angles are supplementary. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (Their measures total 180°.) So, if one of a parallelogram’s angles 2 2 12345678901234567890123456789012123456789012345678901 measures 65°, then the opposite angle must also measure 65°, while the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two other angles each measure 115°. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 291

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A more difficult question about a non-rectangular parallelogram might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 focus on area. To determine the parallelogram’s altitude, you might need 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to apply the Pythagorean theorem (or one of the side or angle triplets). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 In the figure above, A B i CD and A D i BC. If BC is 4 units long 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and CD is 2 units long, what is the area of quadrilateral A BCD ? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 4 =2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 6 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 6 =2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. Since A BCD is a parallelogram, its area 5 base 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (4) 3 altitude. To determine altitude (a), draw a vertical line segment 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 connecting point A to BC, which creates a 45°-45°-90° triangle. The ratio 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the triangle’s hypotenuse to each leg is =2:1. The hypotenuse A B 5 2. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, the altitude (a) of A BCD is , or =2. Accordingly, the area of 2 2 12345678901234567890123456789012123456789012345678901 =2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A BCD 5 4 3 2, or 4 2. = = 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A non-rectangular parallelogram in which all four sides are congruent 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (called a rhom bus) has the following in common with a square: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Perimeter 5 4s 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Area 5 one-half the product of the diagonals 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Circles 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the GM AT, you’ll need to know the following basic terminology 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving circles: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Circumference: The distance around the circle (its “ perimeter” ). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Radius: The distance from a circle’s center to any point on the circle’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circumference. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Diameter: The greatest distance from one point to another on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle’s circumference (twice the length of the radius). 2 1 2 292 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

N ote

Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Chord: A line segment connecting two points on the circle’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circumference (a circle’s longest possible chord is its diameter, passing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 through the circle’s center). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 You’ll also need to apply the two basic formulas involving circles (r 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 radius, d 5 diameter): 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Circumference 5 2pr, or pd 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Area 5 pr 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 2 12345678901234567890123456789012123456789012345678901 . For the GM AT, you won’t The value of p is approximately 3.14, or 2345678901234567890123456789012123456789012345678901 2 1 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to work with a value for p any more precise. In fact, in most circle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems, the solution is expressed in terms of p rather than numerically. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 With the two formulas, all you need is one value—area, circumference, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 diameter, or radius—and you can determine all the others. For example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Given a circle with a diameter of 6: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 radius 5 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 circumference 5 (2)(3)p 5 6p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 area 5 p (3) 5 9p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If a circle’s circumference is 10p centimeters long, what is the area 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the circle, in square centimeters? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 12.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 5p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 22.5 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. 25p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 10p 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. First, determine the circle’s radius. Applying 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circumference formula C 5 2pr, solve for r : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 10p 5 2pr 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 55r 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, apply the area formula, with 5 as the value of r: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A 5 p~5!2 5 25p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 293

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT circle problem might involve other types of geometric figures as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 well—such as triangles, squares and non-square rectangles, and tangent 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 lines. If you advance, you’ll learn how to handle these hybrid problems. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Coordinate Signs and the Four Quadrants 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 GM AT coordinate geom etry questions involve the rectangular coordinate 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plane (or x y-plane) defined by two axes—a horizontal x -ax is and a vertical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y-ax is. You can define any point on the coordinate plane by using two 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 coordinates: an x -coordinate and a y-coordinate. A point’s x -coordinate is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 its horizontal position on the plane, and its y-coordinate is its vertical 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 position on the plane. You denote the coordinates of a point with (x ,y), 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 where x is the point’s x -coordinate and y is the point’s y-coordinate. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The center of the coordinate plane—the intersection of the x and y 2 2 12345678901234567890123456789012123456789012345678901 axes—is called the origin. The coordinates of the origin are (0,0). Any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point along the x -axis has a y-coordinate of 0 (x ,0), and any point along 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the y-axis has an x -coordinate of 0 (0,y). The coordinate signs (positive or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 negative) of points lying in the four quadrants I-IV in this next figure are as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 follows: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uadrant I (1,1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uadrant II (2,1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Q uadrant III (2,2) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uadrant IV (1,2) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 I 2 12345678901234567890123456789012123456789012345678901 II 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 III IV 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 294 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

Alert!

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that we’ve plotted three different points on this plane. Each point 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 has its own unique coordinates. Before you read on, make sure you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 understand why each point is identified (by two coordinates) as it is. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2345678901234567890123456789012123456789012345678901 2 1 Defining a Line on the Coordinate Plane 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can define any line on the coordinate plane by the equation: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 y 5 mx 1 b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this equation: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The variable m is the slope of the line. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The variable b is the line’s y-intercept (where the line crosses the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y-axis). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The variables x and y are the coordinates of any point on the line. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Any (x ,y) pair defining a point. on the line can substitute for the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 variables x and y. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Determining a line’s slope is often crucial to solving GM AT coordinate 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 geometry problems. Think of the slope of a line as a fraction in which the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 numerator indicates the vertical change from one point to another on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 line (moving left to right) corresponding to a given horizontal change, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 which the fraction’s denominator indicates. The common term used for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this fraction is “ rise-over-run.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 You can determine the slope of a line from any two pairs of (x ,y) 2 12345678901234567890123456789012123456789012345678901 coordinates. In general, if (x 1 ,y 1 ) and (x 2 ,y 2 ) lie on the same line, calculate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the line’s slope as follows (notice that you can subtract either pair from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y2 2 y1 y1 2 y2 2 12345678901234567890123456789012123456789012345678901 slope ~m ! 5 or 2 2 12345678901234567890123456789012123456789012345678901 x2 2 x1 x1 2 x2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In applying the preceding formula, be sure to subtract corresponding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 values! For example, a careless test-taker calculating the slope might 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 subtract y 1 from y 2 but subtract x 2 from x 1 . Also, be sure to calculate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ rise-over-run,” and not “ run-over-rise” —another careless, but common, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 error. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 295

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For example, here are two ways to calculate the slope of the line defined by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two points P(2,1) and Q (23,4): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 421 2 12345678901234567890123456789012123456789012345678901 5 slope ~m ! 5 2 12345678901234567890123456789012123456789012345678901 23 2 2 25 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 124 23 2 12345678901234567890123456789012123456789012345678901 slope ~m ! 5 5 2 12345678901234567890123456789012123456789012345678901 2 2 ~23! 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 A GM AT question might ask you to identify the slope of a line defined by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a given equation, in which case you simply put the equation in the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 standard form y 5 m x 1 b, then identify the m -term. O r, it might ask you 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 to determine the equation of a line, or just the line’s slope (m ) or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y-intercept (b), given the coordinates of two points on the line. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the x y-plane, at what point along the vertical axis (the y-axis) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 does the line passing through points (5, 22) and (3,4) intersect that 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 axis? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 28 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 B. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 3 2 12345678901234567890123456789012123456789012345678901 D. 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 13 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The question asks for the line’s y-intercept (the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 value of b in the general equation y 5 m x 1 b). First, determine the line’s 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 slope: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 slope m 5 y2 2 y1x 2 2 x 1 5 4 2 223 2 5 5 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 5 23 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the general equation (y 5 m x 1 b), m 5 23. To find the value of b, 2 2 12345678901234567890123456789012123456789012345678901 substitute either (x ,y) value pair for x and y, then solve for b. Substituting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the (x ,y) pair (3,4): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 y 5 23x 1 b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 5 23~3! 1 b 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 5 29 1 b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13 5 b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To determine the point at which two non-parallel lines intersect on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 coordinate plane, first determine the equation for each line. Then, solve for 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x and y by either substitution or addition-subtraction. 2 12345678901234567890123456789012123456789012345678901 2 1 2 296 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the standard x y-coordinate plane, the x y-pairs (0,2) and (2,0) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 define a line, and the x y-pairs (22,21) and (2,1) define another 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 line. At which of the following points do the two lines intersect? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4 2 2 12345678901234567890123456789012123456789012345678901 A. , 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 4 2 12345678901234567890123456789012123456789012345678901 B. , 2 12345678901234567890123456789012123456789012345678901 2 3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 3 2 12345678901234567890123456789012123456789012345678901 C. 2 , 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 2 12345678901234567890123456789012123456789012345678901 D. , 2 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 2 2 12345678901234567890123456789012123456789012345678901 E. 2 ,2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. For each line, formulate its equation by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determining slope (m ), then y-intercept (b). For the pairs (0,2) and (2,0): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 022 2 12345678901234567890123456789012123456789012345678901 y5 x 1 b ~slope 5 21! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 220 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 0 5 22 1 b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 25b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The equation for the line is y 5 2x 1 2. For the pairs (22, 21) and (2,1): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 ~21! 1 2 12345678901234567890123456789012123456789012345678901 y5 x 1 b slope 5 2 12345678901234567890123456789012123456789012345678901 2 2 ~22! 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 ~2! 1 b 1 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 05b 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 297

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Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 The equation for the line is y 5 x . To find the point of intersection, solve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 for x and y by substitution. For example: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 x 5 2x 1 2 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 x 5 2 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 x 5 2 12345678901234567890123456789012123456789012345678901 3 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 y 5 2 12345678901234567890123456789012123456789012345678901 3 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 2 12345678901234567890123456789012123456789012345678901 The point of intersection is defined by the coordinate pair , . 2 12345678901234567890123456789012123456789012345678901 3 3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Graphing a Line on the Coordinate Plane 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can graph a line on the coordinate plane if you know the coordinates 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of any two points on the line. Just plot the two points, and then draw a line 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 connecting them. You can also graph a line from one point on the line, if 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 you know either the line’s slope or its y-intercept. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to recognize the value of a line’s slope 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (m ) based on a graph of the line. If the graph identifies the precise 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 coordinates of two points, you can determine the line’s precise slope (and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the entire equation of the line). Even without any precise coordinates, you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can still estimate the line’s slope based on its appearance. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Lines that slope upward from left to right: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A line sloping upw ard from left to right has a positive slope (m ). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A line with a slope of 1 slopes upward from left to right at a 45° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 angle in relation to the x -axis. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A line with a fractional slope between 0 and 1 slopes upward from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 left to right but at less than a 45° angle in relation to the x -axis. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A line with a slope greater than 1 slopes upward from left to right 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 at more than a 45° angle in relation to the x -axis. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 298 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lines that slope downward from left to right: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A line sloping dow nw ard from left to right has a negative 2 12345678901234567890123456789012123456789012345678901 slope (m ). 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A line with a slope of 21 slopes downward from left to right at a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 45° angle in relation to the x -axis. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A line with a fractional slope between 0 and 21 slopes downward 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from left to right but at less than a 45° angle in relation to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x -axis. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A line with a slope less than 21 (for example, 22) slopes down2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ward from left to right at more than a 45° angle in relation to 2 12345678901234567890123456789012123456789012345678901 2 the x -axis. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 299

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Horizontal and vertical lines: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A horizontal line has a slope of zero (m 5 0, and m x 5 0). 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A vertical line has either an undefined or an indeterminate slope 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (the fraction’s denominator is 0). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Parallel lines have the same slope (the same m -term in the general 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation). The slope of a line perpendicular to another is the negative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reciprocal of the other line’s slope. (The product of the two slopes is 1. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 2 12345678901234567890123456789012123456789012345678901 For example, a line with slope is perpendicular to a line with slope 2 . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 3 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Referring to the x y-plane above, which of the following could be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the equation of line P ? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 5 2 12345678901234567890123456789012123456789012345678901 A. y5 x2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 B. x 1 y 5 2 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 C. x 2 y 5 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 D. y 5 x 1 2 12345678901234567890123456789012123456789012345678901 5 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 5 2 12345678901234567890123456789012123456789012345678901 E. y 5 2 x 2 2 1 2 2 2 300 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. N otice that line P slopes downward from left 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to right at an angle greater than 45°. Thus, the line’s slope (m in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation y 5 m x 1 b) , 21. Also notice that line P crosses the y-axis at a 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 negative y-value (that is, below the x -axis). That is, the lines y-intercept (b 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the equation y 5 m x 1 b) is negative. O nly choice (E) provides an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 equation that meets both conditions. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Midpoint and Distance Formulas The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To be ready for GM AT coordinate geometry, you’ll need to know these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two formulas. To find the coordinates of the midpoint of a line segment, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 simply average the two endpoints’ x -values and y-values: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 y y 1 x x 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 and y M 5 1 xM 5 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 23 1 2 1 1 4 12345678901234567890123456789012123456789012345678901 For example, the midpoint between (23,1) and (2,4) 5 , , 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 5 2 12345678901234567890123456789012123456789012345678901 or 2 , . 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might simply ask you to find the midpoint between two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 given points. O r, it might provide the midpoint and one endpoint, and then 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ask you to determine the other point. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the standard x y-coordinate plane, the point M (21,3) is the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 midpoint of line segment whose endpoints A (2,24) and B. What 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 are the x y-coordinates of point B? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. (21,22) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. (23,8) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. (8,24) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. (5,12) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. (24,10) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is E. Apply the midpoint formula to find the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 x -coordinate of point B: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 x 12 2 12345678901234567890123456789012123456789012345678901 21 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 22 5 x 1 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 24 5 x 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 301

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Apply the midpoint formula to find the y-coordinate of point B: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 y 2 4 2 12345678901234567890123456789012123456789012345678901 3 5 2345678901234567890123456789012123456789012345678901 2 1 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 5 y 2 4 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 10 5 y 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To find the distance between two points that have the same x -coordinate 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 (or y-coordinate), simply compute the difference between the two y-values 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (or x -values). O therwise, the line segment is neither vertical nor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 horizontal, and you’ll need to apply the distance form ula, which is actually 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the Pythagorean theorem in thin disguise (it measures the length of a right 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle’s hypotenuse): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 d 5 =~x 1 2 x 2 !2 1 ~y 1 2 y 2 !2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For example, the distance between (23,1) and (2,4) 5. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ~23 2 2!2 1 ~1 2 4!2 5 =25 1 9 5 =34. = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask for the distance between two defined points 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (as in the example above). O r, it might provide the distance, and then ask 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 for the value of a missing coordinate—in which case you solve for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 missing x -value or y-value in the formula. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the distance formula, it doesn’t matter which of the two points (x 1 ,y 1 ) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 signifies, or which point (x ,y ) signifies. But whichever pair you choose 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as (x 1 ,y 1 ), be sure not to inadvertently switch x 1 with x 2 , or y 1 with y 2 . 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 302 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll review the following advanced topics 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 involving plane and coordinate geometry: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Properties of isosceles and equilateral triangles 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Properties of trapezoids 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Properties of polygons (including those with more than four sides) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Relationships between arcs and other features of circles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Relationships between circles and tangent lines 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Relationships created by combining a circle with another geometry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 figure (such as a triangle or another circle) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Properties of cubes, other rectangular solids, and cylinders 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 • Plotting and defining 2-dimensional figures (triangles, rectangles, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and circles) on the x y-plane 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Isosceles Triangles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An isosceles triangle has the following special properties: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Two of the sides are congruent (equal in length). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The two angles opposite the two congruent sides are congruent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (equal in size, or degree measure). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If you know any two angle measures of a triangle, you can determine 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 whether the triangle is isosceles. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 303

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 In the figure above, BC is 6 units long, m ∠A 5 70°, and m ∠B 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 40°. H ow many units long is A B? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A. 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 7 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 9 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. Since m ∠A and m ∠B add up to 110°, m ∠C 5 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 70° (70 1 110 5 180), and you know the triangle is isosceles. What’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more, since m ∠A 5 m ∠C, A B ≅ BC. Given that BC is 6 units long, A B 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must also be 6 units long. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In any isosceles triangle, lines bisecting the triangle’s three angles each 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 bisect its opposite side. The line bisecting the angle connecting the two 2 2 12345678901234567890123456789012123456789012345678901 congruent angles divides the triangle into two congruent right triangles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So, if you know the lengths of all three sides of an isosceles triangle, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can determine the area of the triangle by applying the Pythagorean 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 theorem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Two sides of a triangle are each 8 units long, and the third side is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 units long. What is the area of the triangle, expressed in square 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 units? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 14 2 12345678901234567890123456789012123456789012345678901 B. 12 =3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 3 =55 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. Bisect the angle connecting the two congruent 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sides ( and in DA BC on the following page). The bisecting line is the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 triangle’s height (h), and the triangle’s base, which is 6 units long. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 304 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A B 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can determine the triangle’s height (h) by applying the Pythagorean 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 theorem: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 3 2345678901234567890123456789012123456789012345678901 1 h 5 8 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 h 2 5 64 2 9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 h 5 55 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 h 5 55 = 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A triangle’s area is half the product of its base and height. Thus, the area of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 DA BC 5 55 5 3 55 ~6! = = 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Equilateral Triangles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An equilateral triangle has the following three properties: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. All three sides are congruent (equal in length) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. The measure of each angle is 60°. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 3. 2 12345678901234567890123456789012123456789012345678901 s =3 2 12345678901234567890123456789012123456789012345678901 Area 5 (s 5 any side) 2 12345678901234567890123456789012123456789012345678901 4 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Any line bisecting one of the 60° angles divides an equilateral triangle into 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two right triangles with angle measures of 30°, 60°, and 90°; in other 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 words, into two 1:=3:2 triangles, as shown in the right-hand triangle in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the next figure. (Remember that Pythagorean angle triplet?) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 305

Part III: Q uantitative A bility

www.petersons.com

X-Ref

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 In the left-hand triangle, if s 5 6, the area of the triangle 5 9 3. To = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 confirm this formula, bisect the triangle into two 30°-60°-90° 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 ~1:=3:2! triangles (as in the right-hand triangle in the preceding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 figure). The area of this equilateral triangle is ~2!=3, or =3. The 2 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 = 2 12345678901234567890123456789012123456789012345678901 . area of each smaller right triangle is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, equilateral triangles often appear in problems involving 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circles, as you’ll see later in this chapter. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Trapezoids 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A trapezoid is a special type of quadrilateral. The next figure shows a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 trapezoid. All trapezoids share these properties: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. O nly one pair of opposite sides are parallel (BC i A D ). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. The sum of the measures of all four angles is 360°. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Perimeter 5 A B 1 BC 1 CD 1 A D 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 BC 1 A D 2 12345678901234567890123456789012123456789012345678901 3 altitude (that is, one-half the sum of the two 2 4. Area 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parallel sides multiplied by the altitude). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 306 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, a trapezoid problem might require you to determine either 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the altitude, the area, or both. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To cover the floor of an entry hall, a 1′ 3 12′ strip of carpet is cut 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 into two pieces, shown as the shaded strips in the figure above, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each piece is connected to a third carpet piece as shown. If the 1’ 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 strips run parallel to each other, what is the total area of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 carpeted floor, in square feet? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 46 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 48 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 52.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 56 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 60 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The altitude of the trapezoidal piece is 8. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sum of the two parallel sides of this piece is 12’ (the length of the 1’312’ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strip before it was cut). You can apply the trapezoid formula to determine 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the area of this piece: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12 2 12345678901234567890123456789012123456789012345678901 A 583 5 48 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The total area of the two shaded strips is 12 square feet, so the total area of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the floor is 60 square feet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 A GM AT trapezoid problem might require you to find the trapezoid’s 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 altitude by the Pythagorean theorem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 307

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 B C 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ° 120 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A D 4 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 In the figure above, BC i A D . What is the area of quadrilateral 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A BCD ? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. 5 =2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 9 = 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 27 =3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 27 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 16 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The figure shows a trapezoid. To find its area, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first determine its altitude by creating a right triangle: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B C 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 3√ 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 120° 60 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 A D 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 This right triangle conforms to the 30°-60°-90° Pythagorean angle triplet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thus, the ratio of the three sides is 1:=3:2. The hypotenuse is given as 3, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 3 = 2 12345678901234567890123456789012123456789012345678901 . N ow you can calculate the area of the so the trapezoid’s altitude is 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trapezoid: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 =3 3 =3 27 =3 1 9 2 12345678901234567890123456789012123456789012345678901 ~4 1 5! 5 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 2 4 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 308 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

S D S D S DS D

www.petersons.com

Chapter 8: M ath Review—Geometry

Take It to the Next Level

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Polygons 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Polygons include all plane figures formed only by straight lines. Up to this 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 point, we’ve focused on only two types of polygons: three-sided ones 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (triangles) and four-sided ones (quadrilaterals). N ow take a quick look at 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the key characteristics of all polygons. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A polygon in which all sides are congruent and all angles are congruent is 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 called a regular polygon. But for the GM AT, you don’t need to know the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terminology—just the principle. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can use the following formula to determine the sum of the measures of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 all interior angles of any polygon whose angles each measure less than 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 180° (n 5 number of sides): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (n 2 2)(180°) 5 sum of interior angles 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For regular polygons, the average angle measure is also the measure of 2 12345678901234567890123456789012123456789012345678901 every angle. But for any polygon (except for those with an angle exceeding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 180°), you can find the average angle measure by dividing the sum of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measures of the angles by the number of sides. O ne way to shortcut the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 math is to memorize the angle sums and averages for polygons with 3 2 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sides: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 sides: (3 2 2)(180°) 5 180° 4 3 5 60° 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4 sides: (4 2 2)(180°) 5 360° 4 4 5 90° 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5 sides: (5 2 2)(180°) 5 540° 4 5 5 108° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 sides: (6 2 2)(180°) 5 720° 4 6 5 120° 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 7 sides: (7 2 2)(180°) 5 900° 4 7 ' 129° 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 8 sides: (8 2 2)(180°) 5 1080° 4 8 5 135° 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A GM AT question might simply ask for the measure of any interior angle 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of a certain regular polygon; to answer it, just apply the preceding 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 formula. If the polygon is not regular, you can add up known angle 2 12345678901234567890123456789012123456789012345678901 measures to find unknown angle measures. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 309

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If exactly two of the angles of the polygon shown below are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 congruent, what is the LEAST possible sum of the degree measures 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of two of the polygon’s interior angles? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A. 162° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 174° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 176° 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D, 204° 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 216° 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. The figure shows a hexagon. The sum of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 measures of six angles is 720°. Subtracting the measures of the three 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 known angles from 720° leaves 420°, which is the sum of the measures of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the three unknown angles. Set up an equation, then solve for x : 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 x 1 x 1 x 5 420 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 14 2 12345678901234567890123456789012123456789012345678901 x 5 420 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 x 5 ~420! 5 ~30!~5! 5 150 2 12345678901234567890123456789012123456789012345678901 14 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O f the three unknown angles, two are either 150° each. The other is 120°. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The polygon’s two least possible angles measure 54° and 120°. Their sum 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 is 174°. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Another, more difficult, type of problem requires you to determine the area 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of a polygon, which might be either regular or irregular. To do so, you need 2 2 12345678901234567890123456789012123456789012345678901 to partition the polygon into an assemblage of smaller geometric figures. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 310 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What is the area of polygon A BCD E shown above? 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4 1 2 =3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 3 1 3 = 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. 6 =3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 2 1 6 =2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 8 =2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. Divide the polygon into three triangles as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 1 2 12345678901234567890123456789012123456789012345678901 bh 5 ~2! shown below. The area of each of the two outer triangles 5 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ~2! 5 2. (Their combined area is 4.) Since the two outer triangles are both 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1:1:=2 right triangles, BE ≅ BD , and both line segments are 2 =2 units 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 long. Accordingly, the central triangle is equilateral. Calculate its area:. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 s2 =3 ~2 =2!2 =3 8 =3 2 12345678901234567890123456789012123456789012345678901 5 5 5 2 3 = 2 12345678901234567890123456789012123456789012345678901 4 4 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Thus, the area of the polygon is 4 1 2 =3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Advanced Circle Problems 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 GM AT circle problems sometimes involve other geometric figures as well, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 so they’re inherently tougher than average. The most common such 2 12345678901234567890123456789012123456789012345678901 “ hybrids” involve triangles, squares, and other circles. In the next sections, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll learn all you need to know to handle any hybrid problem. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 311

Part III: Q uantitative A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Arcs and Degree Measures of a Circle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An arc is a segment of a circle’s circumference. A m inor arc is the shortest 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 arc connecting two points on a circle’s circumference. For example, in the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 next figure, minor arc A B is the one formed by the 60° angle from the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle’s center (O ). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A circle, by definition, contains a total of 360°. The length of an arc 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relative to the circle’s circumference is directly proportionate to the arc’s 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 degree measure as a fraction of the circle’s total degree measure of 360°. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 60 1 2 12345678901234567890123456789012123456789012345678901 For example, in the preceding figure, minor arc A B accounts for , or , 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 360 6 2 12345678901234567890123456789012123456789012345678901 of the circle’s circumference. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 An arc of a circle can be defined either as a length (a portion of the circle’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circumference) or as a degree measure. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 312 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Circle O , as shown in the figure above, has diameters of D B and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A C and has a circumference of 9. What is the length of minor arc 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 BC? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 11 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 13 2 12345678901234567890123456789012123456789012345678901 D. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 E. 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. Since A O and O B are both radii, we have 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 isosceles DA O B thus making m∠BA C 5 70°. From this we can find 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m∠A O B 5 40°. DBO C is supplementary to ∠A O B, therefore m∠BO C = 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 140°. (Remember: Angles from a circle’s center are proportionate to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 140 7 2 12345678901234567890123456789012123456789012345678901 the arcs they create.) Since m∠BO C accounts for or of the circle’s 2 12345678901234567890123456789012123456789012345678901 360 18 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7 7 2 12345678901234567890123456789012123456789012345678901 circumference, we have the length of minor arc BC = ~9! . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 18 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Circles and Inscribed Polygons 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 A polygon is inscribed in a circle if each vertex of the polygon lies on the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 circle’s circumference. The next figure shows an inscribed square. The 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 square is partitioned into four congruent triangles, each with one vertex at 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circle’s center (O ). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 313

SD

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Look at any one of the four congruent triangles—for example, DA BO . 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N otice that DA BO is a right triangle with the 90° angle at the circle’s 2 2 12345678901234567890123456789012123456789012345678901 center. The length of each of the triangle’s two legs (A O and BO ) equals 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circle’s radius (r). Accordingly, DA BO is a right isosceles triangle, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 m∠O A B 5 m∠O BA 5 45°, and A B 5 r=2. (The ratio of the triangle’s 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sides is 1:1:=2.) Since A B is also the side of the square, the area of a 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 r 2 12345678901234567890123456789012123456789012345678901 2 2 square inscribed in a circle is ~r or 2! , or 2r . (The area of DA BO is = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 one fourth the area of the square.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can also determine relationships between the inscribed square and the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The ratio of the inscribed square’s area to the circle’s area is 2:p. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The difference between the two areas—the total shaded area—is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 pr 22r . 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 2 12345678901234567890123456789012123456789012345678901 2 ~pr 22r !. • The area of each crescent-shaped shaded area is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The next figure shows a circle with an inscribed regular hexagon. (In a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regular polygon, all side are congruent.) The hexagon is partitioned into 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 six congruent triangles, each with one vertex at the circle’s center (O ). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 314 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Look at any one of the six congruent triangles—for example, DA BO . Since 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 all six triangles are congruent, m∠A O B 5 60°, (one sixth of 360°). You 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 can see that the length of A O and BO each equals the circle’s radius (r). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Accordingly, m∠O A B 5 m∠O BA 5 60°, DA BO is an equilateral triangle, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and A B 5 r. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Applying the area formula for equilateral triangles: Area of DA BO 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3r2 =3 r2 =3 12345678901234567890123456789012123456789012345678901 . The area of the hexagon is 6 times the area of DA BO , or . 2 2 12345678901234567890123456789012123456789012345678901 4 2 2 12345678901234567890123456789012123456789012345678901 You can also determine relationships between the inscribed hexagon and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circle. For example, the difference between the two areas—the total 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3r2 =3 2 2 12345678901234567890123456789012123456789012345678901 shaded area—is pr 2 . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 315

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The figure above shows a square that is tangent to one circle at four 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points, and inscribed in another. If the diameter of the large circle is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 10, what is the diameter of the smaller circle? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5 =3 2 12345678901234567890123456789012123456789012345678901 A. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 2p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 5 =2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 7.5 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The square’s diagonal is equal in length to the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 large circle’s diameter, which is 10. This diagonal is the hypotenuse of a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle whose legs are two sides of the square. The triangle is right 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 isosceles, with sides in the ratio 1:1:=2. The length of each side of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 square 5 , or 5 =2. This length is also the diameter of the small 2 2 12345678901234567890123456789012123456789012345678901 =2 2 12345678901234567890123456789012123456789012345678901 circle. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Tangents and Inscribed Circles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A circle is tangent to a line (or line segment) if they intersect at one and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only one point (called the point of tangency). H ere’s the key rule to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 remember about tangents: A line that is tangent to a circle is alw ays 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perpendicular to the line passing through the circle’s center and the point 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of tangency. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 316 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The next figure shows a circle with center O inscribed by a square. Point P 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is one of four points of tangency. By definition, O P ⊥ A B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, notice the following relationships between the circle in the preceding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 figure and the inscribing square (r 5 radius): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Each side of the square is 2r in length. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 • The square’s area is (2r) , or 4r . 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 • The ratio of the square’s area to that of the inscribed circle is :1. 2 12345678901234567890123456789012123456789012345678901 p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The difference between the two areas—the total shaded area—is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4r2 2pr2 . 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 • The area of each separate (smaller) shaded area is (4r2 2pr2 ). 2 12345678901234567890123456789012123456789012345678901 4 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For any regular polygon (including squares) that inscribes a circle: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The point of tangency between each line segment and the circle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bisects the segment. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Connecting each vertex to the circle’s center creates an array of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 congruent angles, arcs, and triangles. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 317

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For example, the left-hand figure below shows a regular pentagon, and the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 right-hand figure shows a regular hexagon. Each polygon inscribes a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle. In each figure, the shaded region is one of five (or six) identical ones. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the figure above, a circle with center O is tangent to A B at point 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D and tangent to A C at point C. If m ∠A 5 40°, then x 5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 140 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 145 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 150 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 155 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 160 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 318 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. Since A C is tangent to the circle, A C ⊥ BC. 2 2 12345678901234567890123456789012123456789012345678901 Accordingly, DA BC is a right triangle, and m∠B 5 50°. Similarly,A B ⊥ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D O , DD BO is a right triangle, and ∠D O B 5 40°. ∠D O C (the angle in 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 question) is supplementary to ∠D O B. Thus, m∠D O C 5 140° (x 5 140). 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Comparing Circles 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, questions asking you to compare circles come in two 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 varieties. You will be required to do one of the following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Calculate the difference between radii, circumferences, or areas. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Determine ratios involving the two circles and their radii, circum2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ference, and areas. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 To calculate a difference between the radii, circumferences, or areas, just 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 calculate each area or circumference, then subtract. And if the question 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 asks you for a difference between proportionate segm ents of the two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 circles, first find the difference between the circular areas, then calculate 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the fractional portion. N o sweat. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To handle questions involving ratios, you need to understand that the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 relationship between a circle’s radius or circumference and its area is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ex ponential, not linear (because A 5 pr2 ). For example, if one circle’s 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 radius is tw ice that of another, the ratio of the circles’ areas is 1:4 2 2 12345678901234567890123456789012123456789012345678901 [pr2 :p(2r)2 ]. If the larger circle’s radius is three times that of the smaller 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle, the ratio is 1:9[pr2 :p(3r)2 ]. A 1:4 ratio between radii results in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1:16 area ratio (and so forth). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The same proportions apply if you compare circumferences and areas. If 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circumference ratio is 2:1, then the area ratio is 4:1. If the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circumference ratio is 4:1, then the area ratio is 16:1. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 319

Take It to the Next Level

Tip

Chapter 8: M ath Review—Geometry

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 In the figure above, point O lies at the center of both circles. If the 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 length of O P is 6 and the length of PQ is 2, what is the ratio of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 area of the smaller circle to the area of the larger circle? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 A. 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7 B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 C. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9 2 12345678901234567890123456789012123456789012345678901 D. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 16 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5 2 12345678901234567890123456789012123456789012345678901 E. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The ratio of the small circle’s radius to that of 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the large circle is 6:8, or 3:4. Since Area 5 pr , the area ratio is 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 p(3) :p(4) , or 9:16. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 320 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Cubes and Other Rectangular Solids 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT questions about rectangular solids always involve one or both of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 two basic formulas (l 5 length, w 5 width, h 5 height): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Volume 5 lw h 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Surface Area 5 2lw 1 2w h 1 2lh 5 2(lw 1 w h 1 lh) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For cubes, the volume and surface-area formulas are even simpler than for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other rectangular solids (let s 5 any edge): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 2 12345678901234567890123456789012123456789012345678901 Volume 5 s3 , or s 5 =Volume 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Surface Area 5 6s2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might require you to apply any one of the formulas. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Plug what you know into the formula, then solve for whatever 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 characteristic the question asks for. O r, a question might require you to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deal with the formulas for both surface area and volume. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A closed rectangular box with a square base is 5 inches in height. If 2 12345678901234567890123456789012123456789012345678901 the volume of the box is 45 square inches, what is the box’s surface 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 area in square inches? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 45 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 66 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. 78 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 81 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 90 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 321

Part III: Q uantitative A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. First, determine the dimensions of the square 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 base. The box’s height is given as 5. Accordingly, the box’s volume (45) 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5lw , and lw 5 9. Since the base is square, the base is 3 inches long on each 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 side. N ow you can calculate the total surface area: 2lw 1 2w h 1 2lw 5 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (2)(9) 1 (2)(15) 1 (2)(15) 5 78. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A variation on the preceding question might ask the number of smaller 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 boxes you could fit, or “ pack,” into the box that the question describes. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 For instance, the number of cube-shaped boxes, each one 1.5 inches on a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 side, that you could pack into the 3 3 3 3 5 box is 12 (3 levels of 4 cubes, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with a half-inch space left at the top of the box). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A test question involving a cube might focus on the ratios among the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cube’s linear, square, and cubic measurements. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If the volume of one cube is 8 times greater than that of another, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what is the ratio of the area of one square face of the larger cube to 12345678901234567890123456789012123456789012345678901 2 2 that of the smaller cube? 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 16:1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 12:1 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. 8:1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 4:1 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 2:1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The ratio of the two volumes is 8:1. Thus, the 2 2 12345678901234567890123456789012123456789012345678901 3 3 2 12345678901234567890123456789012123456789012345678901 linear ratio of the cubes’ edges is the cube root of this ratio: 8: 1, or = = 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2:1. The area ratio is the square of the linear ratio, or 4:1. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 322 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Cylinders 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The only kind of cylinder the GM AT covers is a “ right” circular cylinder (a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tube sliced at 90° angles). The surface area of a right cylinder is the sum of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the areas of: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. The circular base 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. The circular top 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. The rectangular surface around the cylinder’s vertical face 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (visualize a rectangular label wrapped around a soup can) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The area of the vertical face is the product of the circular base’s 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 circumference (i.e., the rectangle’s width) and the cylinder’s height. Thus, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 given a radius r and height h of a cylinder: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Surface Area (SA ) 5 2pr 1 (2pr)(h) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Given a cylinder’s radius and height, you can determine its volum e by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiplying the area of its circular base by its height: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Volume 5 . pr h 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, a cylinder problem might require little more than a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 straightforward application of formula for either surface area or volume. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As with rectangular-solid questions, just plug what you know into the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formula, then solve for what the question asks. For example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Given a radius of 3 and a height of 7, a right cylinder’s volume 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 p(3)2 (7) 5 63p. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A tougher cylinder problem might require you to apply other math 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 concepts. It also might call for you to convert one unit of measure into 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 another. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 323

Part III: Q uantitative A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O ne hose dispenses water at the rate of one gallon per minute, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 a second hose dispenses water at the rate of 1 gallons per minute. 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 At the same time, the two hoses begin filling a cylindrical tank 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whose diameter is 14 inches and whose height is 10 inches. Which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the following most closely approximates the water level, mea2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 sured in inches up from the tank’s circular base, after 1 minutes? 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 [231 cubic inches 5 1 gallon] 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 3.5 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 4.2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 4.8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 5.6 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. 6.7 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 The correct answer is D. After 1 minutes, the two hoses have dispensed 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a total of 3.75 gallons. Set up a proportion in which 3.75 as a portion of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 the tank’s volume equals the water level after 1 minutes as a portion of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the tank’s height: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3.75 x 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 V 10 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The volume of the cylindrical pail is equal to the area of its circular base 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 multiplied by its height: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 2 12345678901234567890123456789012123456789012345678901 2 h ' V 5 pr ((49)(10) ' 1,540 cubic inches 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 7 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The gallon capacity of the pail 5 1,540 4 231, or about 6.7. Plug this 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 value into the proportion, then solve for x : 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 3.75 2 12345678901234567890123456789012123456789012345678901 5 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 6.7 10 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6.7x 5 37.5 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 x 5 5.6 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 324 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

SD

www.petersons.com

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Coordinate Geometry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To handle GM AT questions involving the standard x y-coordinate plane, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll need to be able to perform the following basic tasks covered earlier 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in this chapter: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Plotting points on the coordinate plane 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Determining the slope of a line (or line segment) on the plane 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Interpreting and formulating the equation of a line 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Finding the midpoint of a line segment 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Finding the distance between two points 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N otice that all these tasks involve points and lines (line segments) only. In 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 this section, you’ll explore coordinate-geometry problems involving 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two-dimensional geometric figures—especially triangles and circles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Triangles and the Coordinate Plane 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, a question might ask you to find the perimeter or area of a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 triangle defined by three particular points. As you know, either calculation 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 requires that you know certain information about the lengths of the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 triangle’s sides. Apply the distance formula (or the standard form of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Pythagorean theorem) to solve these problems. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 O n the x y-plane, what is the perimeter of a triangle with vertices at 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points A (21,23), B(3,2), and C(3,23)? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. 12 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. 2 10 1 2 =3 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 2 12345678901234567890123456789012123456789012345678901 7 1 5 =2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 15 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. 9 1 =41 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 325

Part III: Q uantitative A bility

SD

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The figure below shows the triangle on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 coordinate plane: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A C 5 4 and BC 5 5. Calculate A B (the triangle’s hypotenuse) by the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distance formula or, since the triangle is right, by the standard form of the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Pythagorean theorem: (A B)2 5 4 2 1 5 2 ; (A B)2 5 41; A B 5 =41. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle’s perimeter 5 4 1 5 1 =41 5 9 1 =41. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Since the triangle is right, had the preceding question asked for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 triangle’s area instead of perimeter, all you’d need to know are the lengths 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 of the two legs (A ~4!~5!5 10. C and BC). The area is 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To complicate these questions, the test-makers might provide vertices that 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 do not connect to form a right triangle. (Answering this type of question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 requires the extra step of finding the triangle’s altitude.) O r, they might 2 2 12345678901234567890123456789012123456789012345678901 provide only two points, then require that you construct a triangle to meet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain conditions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 326 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 8: M ath Review—Geometry

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the x y-plane, the x y-coordinate pairs (26,2) and (214, 24) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 define one line, and the x y-coordinate pairs (212,1) and (23, 211) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 define another line. What is the unit length of the longest side of a 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 triangle formed by the y-axis and these two lines? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. 15 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. 17.5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 19 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. 21.5 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. 23 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The correct answer is D. For each line, formulate its equation by 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 determining slope (m ), then y-intercept (b): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For the pairs (26,2) and For the pairs (212,1) and 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (214, 24) (23,211) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 6 3 12 4 2 12345678901234567890123456789012123456789012345678901 y 5 x 1 b (slope 5 ) y 5 x 1 b (slope 5 2 ) 2 12345678901234567890123456789012123456789012345678901 8 4 9 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3 4 2 12345678901234567890123456789012123456789012345678901 2 5 ~26! 1 b 1 5 2 ~212! 1 b 2 12345678901234567890123456789012123456789012345678901 4 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 48 2 12345678901234567890123456789012123456789012345678901 2 5 24 1 b 15 1b 2 12345678901234567890123456789012123456789012345678901 2 3 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 2 16 5 b 1 2 12345678901234567890123456789012123456789012345678901 214 5b 2 12345678901234567890123456789012123456789012345678901 2 215 5 b 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6 5b 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 12345678901234567890123456789012123456789012345678901 The two y-intercepts are 6 and 215. Thus the length of the triangle’s side 2 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 along the y-axis is 21.5. But is this the longest side? Yes. N otice that the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 slopes of the other two lines (l1 and l 2 ) are negative reciprocals of each 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3 4 2 12345678901234567890123456789012123456789012345678901 other: 2 5 21. This means that they’re perpendicular, forming 2 12345678901234567890123456789012123456789012345678901 4 3 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the two legs of a right triangle in which the y-axis is the hypotenuse (the 2 2 12345678901234567890123456789012123456789012345678901 longest side). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 327

S DS D

Part III: Q uantitative A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the preceding question had instead asked for the point at which the two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 lines intersect, to answer the question you would formulate the equations 2 2 12345678901234567890123456789012123456789012345678901 for both lines, then solve for x and y with this system of two equations in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two variables. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Circles and the Coordinate Plane 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A GM AT question might ask you to find the circumference or area of a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 circle defined by a center and one point along its circumference. As you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know, either calculation requires that you know the circle’s radius. Apply 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the distance formula (or the standard form of the Pythagorean theorem) to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find the radius and to answer the question. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the x y-plane, a circle has center (2,21), and the point (23,3) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lies along the circle’s circumference. What is the square-unit area of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the circle? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. 36p 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 81p 2 12345678901234567890123456789012123456789012345678901 B. 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. 41p 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. 48p 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. 57p 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 328 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. The circle’s radius is the distance between its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 center (2,21) and any point along its circumference, including (23,3). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ence, you can find r by applying the distance formula: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 2 2 12345678901234567890123456789012123456789012345678901 ~23 2 2! 1 ~23 2 ~21!! 5 25 1 16 5 41. = = = 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The area of the circle 5 p~=41! 5 41p. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In any geometry problem involving right triangles, look out for the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Pythagorean triplet “ fake-out,” in which you’ll see the correct ratio—but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between the wrong two sides. For instance, in the preceding problem, the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 lengths of the two legs of a triangle whose hypotenuse is the circle’s radius 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are 4 and 5. But the triangle does not conform to the 3:4:5 Pythagorean 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 side triplet! Instead, the ratio is 4:5: 41. = 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 329

Take It to the Next Level

Alert!

Chapter 8: M ath Review—Geometry

PART

IV Verbal Ability Critical Reasoning

332

Sentence Correction Reading Comprehension

380 429

PART IV

Chapter

9 Critical Reasoning 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to GM AT Critical Reasoning. In this chapter, you’ll: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Briefly review the basic terminology you need to know for GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn a step-by-step approach to handling any Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn how to recognize and handle each of the three basic, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most common, types of Critical Reasoning questions. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn success keys for tackling Critical Reasoning questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Need-to-Know Terminology 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For GM AT Critical Reasoning, you won’t need to know the technical 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 terminology of formal logic, except for a few basic terms. H ere are the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ones you should know before you proceed any further. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ARGUMEN T: The process of reasoning—from premises to conclusion. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 PREMISE: A proposition helping to support the argument’s conclu- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sion; premises form the basis on which reasoning proceeds; premises 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 are often signaled with words and phrases such as since, because, and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 given that. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ASSUMPTION : Something taken for granted to be true in the argument; 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strictly speaking, assumptions are actually unstated, assumed premises. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CON CLUSION : A proposition derived by inference from the premises 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of an argument. Conclusions are typically signaled by words and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrases such as hence, as a result, consequently, therefore, and it 2 2 12345678901234567890123456789012123456789012345678901 follow s that. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 IN FEREN CE: The process of deriving, from assumed premises, either 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the strict logical conclusion or a conclusion that is to some degree 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 probable. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 332

Chapter 9: Critical Reasoning

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t get hung up on precise dictionary definitions. The GM AT won’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ask you to define terms or try to trick you based on semantics; that’s not 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 what the GM AT is about. But, the test-makers w ill use these terms in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrasing Critical Reasoning questions—so you should have at least a 2 12345678901234567890123456789012123456789012345678901 layperson’s understanding of what they mean. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning—Your 6-Step Game Plan 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The first task in this chapter is to learn the six basic steps for handling a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Critical Reasoning question. You’ll apply these steps to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following sample question: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Among customers of breakfast restaurants, more order fresh fruit for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 breakfast than any other menu item. H owever, a recent health- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 research report indicates that eating eggs does not pose as significant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a health risk as previously thought. In response to this report, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 operators of breakfast restaurants should increase the number of eggs 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but decrease the amount of fresh fruit they order from their suppliers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following, if true, would be the best reason to reject 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the recommendation made in the argument above? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Eating eggs still poses a substantial health risk, especially for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 males over age fifty. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. M ost fresh fruits are available only seasonally, whereas eggs 2 12345678901234567890123456789012123456789012345678901 2 are available any time of the year. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Alternatives to breakfast egg dishes, such as pancakes and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cereals, are growing in popularity at breakfast restaurants. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. M any customers of breakfast restaurants who order eggs also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 order fresh fruit. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. Compared to fresh fruits, pre-prepared fruit juices are growing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in popularity among people who dine at breakfast restaurants. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: Read the question “stem” (the actual question or prompt 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that follows the passage). Reading the question stem first will tell you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what you should think about as you read the passage. Be sure you 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 understand the specific task that the question is asking you to perform. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Step 2: Read the passage and identify its key elements. Identify the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument’s conclusion (if any) and its premises. If the passage contains a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion (most Critical Reasoning passages do), try to follow the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument’s line of reasoning from premise(s) to conclusion. To help 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yourself along, try reading the passage again, starting with the conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (Critical Reasoning passages are brief, so a second reading won’t take 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 much time.) 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 333

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 3: Try to formulate your own answer to the question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Read the five answer choices, looking for one that provides 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 something similar to one of the “best” answers you’ve formulated. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But, don’t assume that your home-grown “ best” answer will look exactly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the way you imagined it. Just look for a choice that conveys the same 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 general idea. Also, keep an open mind to a possible “ best” answer that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hasn’t yet occurred to you. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Step 5: If you’re still not sure what the best answer choice is, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 eliminate whichever ones you can. Eliminate choices that make no 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sense to you, that don’t seem directly relevant to the argument, or that 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 accomplish just the opposite of what the question asks for. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 6: Compare the quality of the remaining (viable) answer 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices. Try to determine which is qualitatively better than the others. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Don’t try to make ultra-fine semantic distinctions, parse words, or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 second-guess the test-makers. The qualitative difference between the best 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and any runner-up choice will be clear enough—if your thinking is straight 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enough. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow let’s walk through the sample question about breakfast restaurants, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using this 6-step approach. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: This question stem tells you quite a bit about the passage as well 2 2 12345678901234567890123456789012123456789012345678901 as what to look for in a viable answer choice. The stem essentially asks you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to recognize how the argument can be weakened. Since it refers to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ argument above,” you know that the passage will contain at least one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 premise (information that you should assume is factual) as well as a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 conclusion, which, in this case, will be in the form of a “ recommenda- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: The passage’s last sentence expresses the argument’s conclusion, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 while the first two sentences indicate the premises on which the conclusion 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is based. So, what’s the line of reasoning here; in other words, what’s the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 logical connection between the premises and the recommendation? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Apparently, the passage’s author thinks that breakfast-restaurant custom- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ers now know that its okay to eat eggs, so a significant number will begin 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ordering eggs instead of (as a substitute for) fresh fruit; based on this 2 12345678901234567890123456789012123456789012345678901 2 reasoning, it would make sense for restaurants to get ready for the shift in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 demand toward eggs and away from fresh fruits—by adjusting their 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supplies accordingly. If you find this line of reasoning a bit questionable — 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in other words, if you think it’s full of holes—you’re on the right track! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Proceed to Step 3. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 334 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 3: The question essentially asks how you’d weaken the argument. So 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now’s the time to critique it—to shoot some big holes in it. Ask yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what else is needed to justify the recommendation, based solely on the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 premises. Doesn’t the logical leap from premises to conclusion rely on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain assumptions about a significant number of breakfast-restaurant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 patrons? H ere are three such assumptions (have any of these occurred to 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you?): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Customers are actually aware of the report (otherwise, why 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 anticipate increased demand for eggs?). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Customers would prefer eggs over fresh fruit, even if they knew 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 about the report (otherwise, why anticipate a shift in demand from 2 2 12345678901234567890123456789012123456789012345678901 fresh fruit to eggs?). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Customers consider eggs a suitable substitute for fresh fruit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (otherwise, why decrease the supply of fresh fruit?). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Any one of these assumptions would form a good basis for a “ best” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer to the question. To draft that best answer, all you’d need to do is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refute any one of those assumptions—in other words, point out that any of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the following is true: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Customers are not aware of the report. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Customers would not prefer eggs over fresh fruit (even if they 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 knew about the report). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Customers do not consider eggs a suitable substitute for fresh fruit. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 4: N otice that the statement in choice (D) (M any custom ers of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 break fast restaurants w ho order eggs also order fresh fruit) is not quite the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 same as saying that eggs are not a substitute for fresh fruit (the last of our 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 home-grown answers from Step 3). Yet, the essence of the critique is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 essentially the same: It’s unfair to assume, without any supporting 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 evidence, that a significant number of customers are going to switch from 2 12345678901234567890123456789012123456789012345678901 fruit to eggs. N otice that (D) uses the word “ many,” leaving open the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possibility that for som e customers, these two choices might be mutually 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exclusive. So does that mean that there’s probably a better answer choice? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N o; it’s a pretty safe bet that (D) is the best choice. But go ahead and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 consider the other choices, anyway, just in case. Tentatively earmark (D) as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your selection, then continue to Step 5. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 5: Consider each of the other four answer choices in turn: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (A) also tends to weaken the argument. (If eating eggs is risky, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 this fact would tend to discourage, rather than encourage, people from 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 eating them.) But if (A) is to significantly weaken the argument, we 2 12345678901234567890123456789012123456789012345678901 1 need to assume that a significant percentage of breakfast-restaurant 2 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 335

Part IV: Verbal A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 customers are males over the age of fifty. Since (A) depends heavily on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this additional assumption, it is not as effective as (D) in weakening the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument. Earmark it as a “ runner-up.” 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Choice (B) is difficult to assess without more information, isn’t it? The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fact that fresh fruits are seasonal might have a bearing on whether 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 owners should decrease their fruit supplies at a particular time. (For 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example, you could argue that, when fresh fruit is plentiful, lowering 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the supply might be safer than when it is not.) But what does that have 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 to do with increasing egg supply? Absolutely nothing. As you can see, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it’s a real stretch to defend (B) as directly relevant to the argument at 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 all, let alone as a statement that would clearly weaken the argument. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Eliminate it! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) provides a reason why restaurant owners might want to 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 decrease their supply of eggs. So (C) does tend to weaken the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument. But (C) helps refute only half of what the argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 recommends. What about the recommendation to decrease fresh fruit 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supplies? Whether alternatives to eggs are gaining in popularity has no 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear relationship on the demand for fresh fruit. So earmark (C) as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another “ runner-up.” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) provides a reason why restaurant owners might want to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decrease their supply of fresh fruit—which is part of what the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument recommends. So (E) actually tends to support, or strengthen, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the argument—just the opposite of what you’re looking for in the best 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice. Eliminate (E)! 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 6: Reflect again on the three most viable choices—the ones that tend 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to weaken the argument. N otice that choices (A) and (C), the two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 runners-up, both pale in comparison to (D) in terms of how seriously they 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weaken the argument. You can confidently confirm your selection: (D). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the preceding question, the difference between (D), the best choice, and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the two runner-up choices, (A) and (C), is just the degree of qualitative 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difference that’s typical of the GM AT. O n the actual exam, you won’t 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to make judgment calls that are any closer than the ones made here. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 336 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Assumption Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In an assumption question, the passage will contain a series of premises 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and a conclusion. H owever, in order for the argument’s conclusion to be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probable, at least one additional premise must be assum ed. In other words, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the argument will rely on at least one assum ption. Your task is to identify 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 which of the five answer choices indicates an assumption. Think of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 structure of the argument this way: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 A rgum ent: stated premise(s) 1 assumption → inference (conclusion) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You know you’re dealing with an assumption question when the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stem looks something like one of the following (a question stem might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refer to specific passage information as well): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The argument in the passage depends on which of the following 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 assumptions?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Which of the following is an assumption that enables the conclusion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above to be properly drawn?” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The conclusion drawn in the first sentence logically depends on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which of the following assumptions?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 How to Identify an Argument’s Assumptions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To identify an argument’s assumptions, always ask yourself this question: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ In addition to the stated premises, what m ust be assumed as factual to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 justify the argument’s logical leap from premises to conclusion—for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the conclusion to be probable?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Try asking and answering this question for Arguments 1 and 2 below. For 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each argument, try to think of at least one or two assumptions, then jot 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them down on paper. (O n the GM AT, premises and conclusions are not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 labeled as they are here.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument 1: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: M ore new Jupiter M otors automobiles were sold this 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 year than any other brand. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise: Jupiter M otors automobiles have the lowest sticker 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 prices, which are the manufacturers’ suggested retail prices, of any 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 new automobiles on the market. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Conclusion: Consumers rank low purchase price as the most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 important factor when purchasing new automobiles. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 337

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 2: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Three years ago a business tax credit for research and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 development was enacted into law for the purpose of stimulating 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 these business activities. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: O verall business profits have risen steadily since the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 enactment of this law. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: The tax credit has failed to achieve its objective of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 stimulating research and development. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow read the following assumptions. Think about each assumption until 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you understand the necessary link it provides in the argument’s chain of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning—from premises to conclusion. Without the assumption the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument falls apart, doesn’t it? 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A ssum ption (A rgum ent 1): Comparative sticker prices coincide with 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 comparative prices consumers actually pay for new automobiles. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A ssum ption (A rgum ent 2): N ew investment in research and develop- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment does not generally enhance business profits within a brief 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (three-year) period. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Did you identify these necessary assumptions, or did you instead jot down 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 various propositions that merely lend additional support to the argument, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 such as the ones below? Any of these propositions, if factual, m ight lend 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 support to the argument, rendering its conclusion more probable. Yet the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument would not fall apart without them, would it? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Additional supporting evidence (Argument 1): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The supply of new automobiles other than Jupiter M otors auto2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mobiles is sufficient to meet demand for them. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Jupiter M otors salespeople are no more adept at salesmanship 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than salespeople who sell other automobiles. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Warranties, service contracts, and other purchase incentives 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 besides sticker price are no more attractive for Jupiter M otors 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 automobiles than those of other brands. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Jupiter M otors automobiles provide no advantage over other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 brands with respect to features other than price—such as safety, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 functionality, and appearance. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Additional supporting evidence (Argument 2): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The tax credit is small compared to the costs of new research and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 development. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 338 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The general economic climate for business has remained at least as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 healthy as it was three years ago. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Taxes on businesses have otherwise remained at current levels or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 declined during the same time period. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • M ajor corporate research initiatives begun prior to the enactment 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 of the law began to enhance profits during the last three years. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Be sure you understand the qualitative difference between necessary 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 assumptions and merely helpful additional evidence. Why? In any G M AT 2 2 12345678901234567890123456789012123456789012345678901 assum ption question, the best answ er choice w ill provide a necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assum ption. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Assumption questions have a lot in common with the GM AT 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument-Analysis section, where your primary task is to identify the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument’s assumptions. The key difference is that you write your own 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 response rather than pick one among five choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A Typical Assumption Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to identify and distinguish between necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions and other supporting evidence, attempt the following 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT-style assumption question. (This one is a bit easier than average.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you tackle the question, follow these steps: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the argument’s conclusion and premises. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Try to identify at least one necessary assumption and jot it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 down—before reading the answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Scan the answer choices for that assumption—or one similar to it. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Earmark other choices you think provide supporting evidence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. For each remaining answer choice, ask yourself why it is not a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 viable choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Then read the analysis of the question and of each answer choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For several consecutive years, poultry prices at each of three statewide 2 12345678901234567890123456789012123456789012345678901 grocery-store chains have exceeded the national average by about fifty 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 percent. Also, the per-pound difference in poultry prices among the three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stores never amounted to more than a few pennies, while among grocery 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stores in other states, the prices varied by nearly a dollar over the same 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 period. The three chains must have conspired to not compete among 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 themselves and to fix their poultry prices at mutually agreed-upon levels. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 339

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The claim that the three grocery-store chains conspired to fix 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 poultry prices rests on which of the following assumptions for the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time period referred to above? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. N o other grocery store charged higher prices for poultry other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than the three chains. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. Average poultry prices in the state where the three chains 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 operate exceeded the national average. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. The price that grocery stores paid for poultry did not vary 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 significantly from state to state. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Consumers in the state where the three chains operate gener12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 ally prefer poultry over other meats, even if poultry is more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expensive than other meats. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. O ther grocery stores operating in the same state as the three 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 chains also sell poultry to consumers. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The argument relies on the assumption that all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 other possible factors in the price grocery stores charge for poultry were 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essentially the same in the state where the three chains operate as in other 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 states. O ne such factor is wholesale price (the price grocery stores pay 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suppliers for poultry). A higher wholesale price generally leads to higher 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prices for consumers. Answer choice (C) expressly eliminates this factor. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Admittedly, an “ ideal” answer choice would provide a more sweeping 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement—that all factors possibly affecting poultry price were the same 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from state to state. N evertheless, (C) is the only answer choice that serves 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to affirm the assumption; thus (C) is the best choice. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) admittedly provides som e support for the argument. H igher 2 2 12345678901234567890123456789012123456789012345678901 poultry prices at another store would weaken the argument that the three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 chains conspired to fix prices; thus given the inverse—that no other store 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 charges higher poultry prices—the argument’s conclusion becomes more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probable. H owever, (A) is not a necessary assumption. Even if a certain 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 grocery store charged higher prices for poultry during the period, this fact 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 would probably not be statistically significant in light of the much lower 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 national average—especially if that store were located in another state and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 therefore did not compete with the three chains. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (B) actually serves to w eak en the argument. Given (B), the greater 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the number of other grocery stores in the same state the more likely that 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these other stores also charged high prices for poultry. This fact would in 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 turn help refute the claim that the three chains were motivated by any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concern other than to compete effectively against other stores in the state. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is not relevant to the argument, which is concerned with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 poultry prices charged by the three chains compared to poultry prices in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 other states, not compared to prices of other meats. 2 340 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (E) actually w eak ens the argument. The more competitors, the less 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 likely these three chains together hold a statewide poultry monopoly. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (M onopolists are more likely to charge whatever price they wish for their 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 products.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Assumption Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1. Formulate your own “ best” answer as your read the passage—by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 filling in the missing logical link between the argument’s premises 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and its conclusion. If you know what to look for among the five 2 2 12345678901234567890123456789012123456789012345678901 answer choices, you’ll be more likely to find it, and less likely to fall 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 prey to the test-maker’s wrong-answer ploys. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Don’t spend too much time brainstorming; if the missing link (a nec2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 essary assumption) doesn’t occur to you within 10 or 15 seconds, go 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ahead and read the answer choices. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. If a necessary assumption occured to you as you read the passage, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 scan the answer choices quickly for it (or a statement similar to it). If 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you spot it, immediately select it (click on the button to the left of it) 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 as your tentaive choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. If more than one answer choice seems viable to you, for each choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ask yourself whether the proposition provides a link in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument’s chain of reasoning. If it doesn’t, eliminate that answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice even if it lends support to the argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. Look out for the following types of wrong answers (in addition to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 those that provide supporting but unessential additional evidence): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Additional information that serves to w eak en the argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 • Superfluous information, which is not directly relevant to the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Additional-Evidence Questions—Weakening 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this type of question, the passage will look just like a passage for an 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 assumption question; the passage will contain a series of premises, along 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with a conclusion whose probability depends on one or more assumptions. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the basic structure again: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A rgum ent: stated premise(s) 1 assumption(s) → inference (conclusion) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In a weakening-evidence question, however, your task is to identify which 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the five answer choices m ost seriously w eak ens the argument. You 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know you’re dealing with an weakening-evidence question when the 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 341

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 question stem looks similar to one of the following (a question stem might 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refer to specific passage information as well): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Which of the following, if true, would most weaken the argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The argument in the passage would be most seriously weakened if it 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 were true that” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following, if true, is most damaging to the conclusion 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 above?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following statements, if true, provides the best evidence 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 that the reasoning in the argument above is flawed?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Each of the following, if true, raises a consideration against the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion above, EXCEPT:” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Your task here is to identify the only answer choice that does N O T 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weaken the argument.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How to Weaken an Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To understand how an argument by inference can be weakened, consider 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 1 on page 337. H ere it is again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: M ore new Jupiter M otors automobiles were sold this 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 year than any other brand. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Jupiter M otors automobiles have the lowest sticker 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 prices, which are the manufacturers’ suggested retail prices, of any 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 new automobiles on the market. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Conclusion: Consumers rank low purchase price as the most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 important factor when purchasing new automobiles. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 There are many ways to weaken an argument like the one above. O ne way 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is to essentially point out as a matter of fact that the conclusion is false, or 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that a stated premise needed for the conclusion to be probable is false. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H owever, in a GM AT weakening-evidence question, you’re unlikely to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find either method among the five choices—because both are bit too 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 obvious. Instead, the test-makers prefer the following two methods: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Directly refute a necessary assumption—in other words, provide 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evidence that the assumption is false as a matter of fact. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ew automobiles with comparatively high sticker prices are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 often sold to consumers for less than automobiles with lower 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sticker prices. 2 12345678901234567890123456789012123456789012345678901 2 1 2 342 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Refute other possible supporting evidence—evidence that does 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not pertain directly to a necessary assumption but that, if true, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 would nevertheless increase the conclusion’s probability. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Ex am ple A : Production at the plants of Jupiter M otors’ main 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 competitor has been hampered by numerous labor strikes 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 during the last three years. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Example B: Warranties and other non-price purchase incen12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 tives vary widely among retailers of new automobiles. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s what you need to know about these two methods when analyzing a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT weakening-evidence question: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A method-1 answer choice is always better than a method-2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice, because the former is a direct attack on a necessary 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 assumption. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • If no method 1 proposition appears among the answer choices, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then the best choice will be the best among the method-2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 propositions listed. (Ex am ple A above would be a better choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than Ex am ple B. Why? Ex am ple B leaves open the possibility 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that non-price incentives at Jupiter retailers are less attractive 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 than at other retailers, which would actually strengthen the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In weakening-evidence questions, don’t expect any answer choice to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 directly refute or contradict the Argument’s conclusion or one of its 2 12345678901234567890123456789012123456789012345678901 premises. Although either method is a great way to annihilate an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument, the choice would be too easy to spot as the best one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A Typical Weakening-Evidence Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to weaken an Argument, and distinguish 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 between propostions that merely weaken and those that completely 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 undermine the Argument, take another look at the GM AT-style question 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you encountered near the beginning of this chapter. (This question is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 average in difficulty level.) This time around, as you tackle the question, 2 2 12345678901234567890123456789012123456789012345678901 do the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Identify the argument’s conclusion and premises. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Try to identify at least one necessary assumption and jot it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 down—before reading the answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Scan the answer choices for a proposition that directly refutes, or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contradicts, that assumption. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 343

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Earmark other choices you think serve to weaken the Argument— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then rank them in quality (degree of damage to the conclusion). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. For each remaining answer choice, ask yourself why it is not a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 viable choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then read the analysis of the question and of each answer choice. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Worldwide retail sales of home entertainment systems, which 2 12345678901234567890123456789012123456789012345678901 include a television and an audio system, increased twenty-five 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 percent this year over last year. At the same time, worldwide retail 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sales of new automobiles declined by about the same percent. These 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 statistics show that consumers can no longer afford to purchase 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both types of products during the same year. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following, if true, would cast most serious doubt on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the conclusion drawn above? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. Fewer advertisements for new cars appeared on television 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during the most recent year than during the previous year. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. Consumers are spending more money on home entertainment 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 systems than on new cars. 2 12345678901234567890123456789012123456789012345678901 C. People who own home entertainment systems do not drive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their automobiles as often as other people. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. Prices of home entertainment systems and new cars were 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 higher during the most recent year than during the previous 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 year. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The reliability of automobiles this year improved significantly 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 over last year. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The argument relies on the assumption that all 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other possible factors influencing consumers’ buying decisions respecting 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the two products remained unchanged from last year to this year. An ideal 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ best” answer would directly refute or provide strong evidence against this 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 assumption. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) accomplishes this better than any other choice—by providing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an alternative explanation for the fact that consumers are buying fewer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 new cars and more entertainment centers. Specifically, if a car is more 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reliable, then it is less likely to be replaced by a new one. By the same 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 token, if people keep their cars longer and do not need to spend much 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 money to repair them, then people can better afford to purchase other 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 consumer items such as entertainment centers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) might explain why sales of new cars have declined. H owever, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (A) does not explain increased sales of home entertainment centers. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 344 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (B) reinforces the argument’s premise, thereby strengthening the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) is irrelevant to the argument. (C) provides a reason why people 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with home entertainment systems might replace their cars less often. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H owever, even if this were the case, it would have no bearing on whether 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 these people can afford both items. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) does not explain why consumers have chosen one type of 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 product over another. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Tips for Tackling Weakening-Evidence Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. As you read the passage try to identify at least one necessary 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumption. There are two general types of assumptions that are 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 especially common in weakening-evidence arguments: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The assumption that all other factors are equal—if the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The assumption that all other relevant conditions rem ain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unchanged over tim e, if the argument seeks to explain or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 predict change from one point in time (or period of time) to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 another 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Scan the answer choices for a proposition that directly refutes an 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 assumption. If you spot one, immediately select it (click on the button 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the left of it) as your tentative choice. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. In all likelihood, more than one answer choice will serve to weaken 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the argument. Always select a choice that directly addresses, and 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 attacks, a necessary assumption over any other choice that weakens 2 12345678901234567890123456789012123456789012345678901 2 the argument. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Before confirming your selection, ask yourself whether your choice 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 serves to destroy a logical link needed for a convincing argument; if it 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 doesn’t, look for a better answer choice. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. If no answer choice refutes a necessary assumption (it could happen), 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you’ll need to weigh the comparative quality of all answer choices 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that serve to weaken the argument. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. Look out for the following types of wrong answers: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that affirms a necessary assumption—in other 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 words, that accomplishes just the opposite of what the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question asks for. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 345

Part IV: Verbal A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A statement that serves to strengthen (rather than weaken) the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument in some other way. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that could either strengthen or weaken the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument, depending on additional unknown facts. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that contains superfluous information, which is 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 not directly relevant to the argument. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 When handling a weakening-evidence question, what if no answer choice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hits directly on what you’re sure is a key assumption behind the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument? Don’t assume that your powers of reasoning have failed you. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Perhaps the argument depends on other assumptions as well. O r perhaps 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the particular question wasn’t designed to test you on recognizing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumptions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Additional-Evidence Questions—Supporting 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 the Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 For a supporting-evidence question, your task is to identify which of five 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 propositions provides the m ost support for the argument—just the 2 2 12345678901234567890123456789012123456789012345678901 opposite as for a weakening-evidence question. You know you’re dealing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with a supporting-evidence question when the question stem looks similar 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to one of the following (a question stem might refer to specific passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information as well): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following, if true, most strongly supports the author’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following statements, if true, would most strengthen the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument above?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following, if true, provides the best indication that the 2 2 12345678901234567890123456789012123456789012345678901 conclusion in the argument above was logically well supported?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Which of the following best completes the passage below?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How to Strengthen an Argument 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To understand how an argument by inference can be supported or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 strengthened, consider Argument 2 on page 338. H ere it is again: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 2: 2 12345678901234567890123456789012123456789012345678901 Prem ise: Three years ago a business tax credit for research and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 development was enacted into law for the purpose of stimulating 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these business activities. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 346 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Tip

Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Prem ise: O verall business profits have risen steadily since the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enactment of this law. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: The tax credit has failed to achieve its objective of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stimulating research and development. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 There are tw o methods of strengthening an argument like this one (the first 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 is more effective): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1. Provide a necessary assumption (assert it is factual) or provide 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 strong evidence that it is factual. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ex am ple: Investing in research and development does not 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 generally enhance profitability until several years after the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 investment. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2. Provide evidence that adds weight or credibility to the argument, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but that does not affirm a necessary assumption. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ex am ple A : Costs of certain raw materials used in many areas 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of research and development have increased since the law was 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 enacted. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Ex am ple B: M any large corporations curtailed significant 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 research and development shortly before the law was enacted. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s what you need to know about these two methods for analyzing a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT supporting-evidence question: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A proposition that affirms a necessary assumption (method 1) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provides better support for an argument than one that does not. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • If no method-1 proposition appears among the answer choices, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then the best choice will be the strongest method-2 proposition 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 listed. (Ex am ple A above would be a better choice than Ex am ple 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. Why? The degree of support Ex am ple B lends to the argum ent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 depends entirely on our assum ption that new research and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 developm ent cannot enhance profits w ithin three years; Ex am ple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A lends support to the argument irrespective of this assumption.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The best way to strengthen an argument is to affirm an assumption; the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best way to weaken it is to refute an assumption. If you’re beginning to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 think that assumptions are what GM AT Critical Reasoning is mainly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about, you’re absolutely correct! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 347

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A Typical Supporting-Evidence Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to strengthen an argument and distinguish 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among propositions of varying degrees of support, attempt the following 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 GM AT-style supporting-evidence question. (This one is average in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficulty.) As you tackle the question: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Identify the argument’s conclusion and premises. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Try to identify at least one necessary assumption and jot it 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 down—before reading the answer choices. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Scan the answer choices for a proposition that essentially provides 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 that assumption. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Earmark other choices you think serve to strengthen the argu2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment—then rank them in quality (degree of support). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • For each remaining answer choice, ask yourself why it is not a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 viable choice. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Then read the analysis of the question and of each answer choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In an experiment involving addicted cigarette smokers, each subject 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 was unknowingly administered either the new drug N ico-Gone or a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 placebo. O ne year later, less than a third of the subjects who were 2 12345678901234567890123456789012123456789012345678901 administered N ico-Gone had resumed smoking, compared with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about two thirds of the subjects who were administered a placebo. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These reports confirm that N ico-Gone is effective in curing addic2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion to cigarette smoking. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Which of the following, if true, most strongly supports the conclu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sion above? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. O ne year after the experiment, the percentage of the experi2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment’s subjects who were cigarette smokers was less than the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 percentage of the general population who were smokers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. O ther reliable studies indicate that cigarette smokers often 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 falsely inform others that they are not smokers. 2 12345678901234567890123456789012123456789012345678901 C. During the year following the experiment, cigarettes were 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 readily available to all of the subjects. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. O ne year after the experiment, the total number of subjects 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 who were cigarette smokers was less than the number who 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 were smokers one year prior to the experiment. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. During the year following the experiment, some of the subjects 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 received other treatment to help them avoid cigarette smoking. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 348 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The argument relies on the major unstated 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 assumption that no factor other than the experiment at issue was 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 responsible for the reported result one year after the experiment. (C) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 provides evidence that lends credence to this assumption. If cigarettes were 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unavailable to some of the subjects during the year, this fact would be the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 primary explanation for any decrease in the number of smokers among 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the subjects. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) does lend som e measure of support to the argument. H owever, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (A) fails to provide the specific difference between the two percentages; a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 small percentage would not be statistically significant, especially if the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 number of subjects participating in the experiment was small. Thus, (A) is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 qualitatively not as strong as (C). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (B) actually w eak ens the argument, by providing evidence that the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 results as reported by the subjects themselves might have been unreliable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (D) fails to provide sufficient information to support the argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Specifically, (D) fails to distinguish between the subjects receiving 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ico-Gone and those receiving the placebo. (D) also fails to account for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the possibility that the number of subjects who smoked might have 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 changed significantly during the year immediately preceding the experi- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ment. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) actually w eak ens the argument by providing evidence that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 some factor other than N ico-Gone might have been responsible for the 2 12345678901234567890123456789012123456789012345678901 22 reported results. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Supporting-Evidence Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. As you read the passage, try to identify a necessary assumption. There 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 are two general types of assumptions that are especially common in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supporting-evidence questions: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The assumption that all other factors are equal—if the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 argument seeks to explain certain differences between two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phenomena 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The assumption that all other relevant conditions rem ain 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unchanged over tim e—if the argument seeks to explain or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 predict some sort of change from one point in time (or period 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of time) to another 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Scan the answer choices for a proposition that provides that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 assumption. If you spot it, immediately select it (click on the button 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the left of it) as your tentative choice. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 349

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. In all likelihood, more than one answer choice will serve to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strengthen the argument. Always select a choice that directly affirms 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a necessary assumption over any other choice. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4. If no answer choice affirms a necessary assumption, you’ll need to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 weigh the comparative quality of all answer choices that serve to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 strengthen the argument. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. Look out for the following types of wrong answers: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • A statement that weakens rather than strengthens the 2 12345678901234567890123456789012123456789012345678901 2 argument 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • A statement that could either strengthen or weaken the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument, depending on additional unknown facts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that contains superfluous information, which is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not directly relevant to the argument 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Inference Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 For a GM AT inference question, the passage will simply provide a series of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 premises—information that you are to accept as factual. Your task is to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 identify among the five answer choices the statement that provides the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 most reliable, or probable, conclusion from the passage information. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Expect to encounter at least one or two questions of this type on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You know you’re dealing with an inference question when the question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stem looks similar to one of the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following statements draws the most reliable conclusion 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from the information above?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following conclusions about . . . is best supported by the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage?” 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Which of the following can most properly be inferred from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information in the passage above?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that each of these question stems contains the word “ most” or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ best.” These are important words. For an inference question, even the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best answer choice will not necessarily follow from the premises; yet it will 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be m ore probable than any other answer choice. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 350 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Arguments in which conclusions are necessarily either true or false 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 involve deductive reasoning. GM AT necessary-inference questions are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinct, which you’ll discover if you advance to the N ext Level. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 How to Identify a Strong Inference 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 H ow do you recognize a probable, or reliable, inference among five 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices and distinguish it from less reliable ones? The best way to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer this question is by example. Consider the following two 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 GM AT-style passages. After reading each one, ask yourself: “ Given this 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information, what else is probably true?” Try to think of at least one 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer—then jot it down as if you were drafting your own best answer 2 2 12345678901234567890123456789012123456789012345678901 choice for a GM AT inference question. (Expect an easier time with passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1 than 2.) 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Passage 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any sociologists argue that science-fiction television program s play 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 a crucial role in fostering the belief that intelligent aliens have visited 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Earth. H ow ever, in countries w here relatively few people have access 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 to television, belief that intelligent aliens have visited Earth is at least 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as prevalent as in other countries. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Passage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To subsidize the profits of dom estic farm s that grow a certain crop, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 country X im poses a tariff on ex ports of the crop. A s a result, foreign 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 food-product m anufacturers that m ust use the crop in their products 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 find it m ore difficult to com pete w ith country X businesses that m ust 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 use the sam e crop in their products. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext, for each passage read the following conclusions (inferences). Think 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about each one until you understand that the one listed as a possible best 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choice m ak es sense; in other words, that it is reasonably inferable 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from the passage and probable to som e degree. Then compare it to the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ones listed as typical wrong-answer choices. N otice that each of these 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unreliable inferences depends on additional, unsubstantiated assumptions, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and is therefore far less probable. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 351

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Conclusions (inferences) from Passage 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 R eliable inference (potential “best” answ er choice): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Science-fiction television programs are not the only factor in determin- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ing whether a person believes intelligent aliens have visited Earth. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Unreliable inferences (typical w rong-answ er choices): 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Science-fiction television programs do not affect whether people 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 believe that intelligent aliens have visited Earth. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • People who do not watch television are more likely to believe that 2 12345678901234567890123456789012123456789012345678901 2 intelligent aliens have visited Earth than people who do. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Science-fiction television programming is not realistic enough to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 persuade people that intelligent aliens have visited Earth. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Conclusions (inferences) from Passage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 R eliable inference (potential “best” answ er choice): 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Importing the crop from country X is less costly for foreign businesses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than if these businesses obtain the crop from another source. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Unreliable inferences (typical w rong-answ er choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • The farms of country X are the only sources of the crop. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O ther countries that produce the crop also impose export tariffs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the crop. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 • The total demand for the crop produced in country X declined as a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 result of the export tariff. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Compare the reliable inferences to the unreliable ones listed above. N otice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the unreliable ones either depend on additional assumptions that find 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 no support in the passage and/or go too far—beyond the reliable inference 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to one that amounts to a sweeping, all-encompassing conclusion. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 A Typical Inference Question 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to identify and distinguish between reliable and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unreliable inferences, attempt the following GM AT-style inference ques- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion, which is average in difficulty. As you tackle the question, follow 2 2 12345678901234567890123456789012123456789012345678901 these steps: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Try to answer the question “ What else is probably true” after 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reading the passage, but before reading the answer choices. If you 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 think of an answer, jot it down. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2. Scan the answer choices for your answer, or one similar to it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 352 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. If there’s no answer choice similar to the one you thought of, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 analyze each one in turn to determine how strongly the passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supports it. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 4. For each statement you eliminated, be sure you can think of an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional assumption needed for the statement to make sense as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 a conclusion. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Then, read the analysis of the question and of each answer choice. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 During each of the last five years, both the demand for beverage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 containers and the quantity of beverage containers recycled to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 produce new beverage containers have increased steadily. At the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 same time, the number of freshly cut trees used to produce beverage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 containers has declined each year. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the statements above are all true, they provide most support for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which of the following conclusions about the last five years? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. The number of new beverage containers not made of recycled 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 materials has decreased. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. M ore beverage containers have been recycled for producing 2 12345678901234567890123456789012123456789012345678901 new beverage containers than have not been recycled for this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 purpose. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. Recycled beverage containers have been used only for making 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 new beverage containers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. The number of beverage containers made of tree materials has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decreased. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. The number of used beverage containers not being recycled has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decreased. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is A. The fact that the number of recycled beverage 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 cotainers has been increasing while the number of new trees used to make 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 beverage containers has been declining lends considerable support to (A). 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 M oreover, (A) allows for the possibilty that some beverage containers are 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 made of recycled materials other than tree materials. Admittedly, demand 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 for beverage containers in general has increased recently, reducing the 2 12345678901234567890123456789012123456789012345678901 likelihood that (A) is true. O n balance, however, (A) is more strongly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supported than any of the other answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (B) is not inferable from the statements, which provide information 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 about changes in numbers from one year to the next, not total numbers. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The passage provides no information which would permit a comparison 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 between the total numbers of recycled beverage containers and non- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recycled beverage containers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 353

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (C) is not inferable. The passage provides no information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 permitting the sweeping inference that the increasing demand for beverage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 containers has been so great as to necessitate the use of all recycled 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 beverage containers to meet this increased demand. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is not inferable. Although the decrease in the number of freshly 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 cut trees each year tends to show that (D) might be true, the increase in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 demand for beverage containers and in the number of recycled beverage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 containers tend to show just the opposite. In any event, (D) also requires 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 more information (additional assumptions) about the percentage of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 beverage containers, both new and recycled, made of tree products. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Choice (E) is not inferable. Just because the number of beverage containers 2 2 12345678901234567890123456789012123456789012345678901 being recycled has increased each year, it is unfair to conclude that the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number of beverage containers not being recycled has been decreasing. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fact, given the increased demand for beverage containers in general, it is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just as likely that consumers are recycling more beverage containers and 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discarding more beverage containers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Inference Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1. All statements in the passage are premises; thus, you should assume 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they are all factual (even if in real life they seem somewhat dubious). 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Remember: Your task is not to recognize what m ust be true, but 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 rather to recognize what’s m ost lik ely to be true among the five 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusions listed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Formulating a possible “ best” answer might help you zero in on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best answer choice. But don’t expect this technique to work as 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reliably for inference questions as for the other question types 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 covered in this chapter. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. If an answer choice makes sense as a conclusion only if additional 2 2 12345678901234567890123456789012123456789012345678901 facts are assumed, you can safely eliminate it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 5. If an answer choice draws a sweeping conclusion—an all- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 encompassing generalization—you can probably eliminate it as the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best answer choice. When in doubt, choose a narrower conclusion 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 over a broader one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 354 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for GMAT Critical Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are some basic tips you should follow for any type of Critical 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Reasoning question—the types you encountered so far in this chapter, as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 well as those you’ll examine if you advance to the N ext level. Apply these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ keys” to Part V’s practice tests, and then review them again just before 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 exam day. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Always Read the Question Stem First 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The question “ stem” refers to the question (or prompt) itself, N O T to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage or the answer choices. Read the stem before reading the passage. It 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will contain useful clues about what to look for and think about as you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 read the passage. (Reading answer choices before reading the passage is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wasted time, because you’ll invariably need to read them again.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Assume That All Premises Are Factual 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you read the passage, assume that all premises—statements asserted as 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 factual—are indeed factual. Critical Reasoning questions are not designed 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to test your real-world knowledge of passage topics. Although the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 premises often resemble real-world facts, whether they are factual is beside 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the point. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Identify the Conclusion to Clear Up Your Confusion 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ost passages will contain a conclusion. The conclusion might appear at 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the beginning, in the middle, or at the end of the passage. If a passage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 confuses you, look for the conclusion, then try to follow the argument’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 line of reasoning from premises to conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Read Every Answer Choice before Confirming Your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Selection 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Remember: the test directions ask you to select the best among the five 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices, and the qualitative difference between the best and second-best 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices can be subtle. Unless you carefully consider all five answer choices, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 you might select the second-best one without even reading the best one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 355

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Critical Reasoning Takes Time; So Pace Yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Accordingly 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For most test-takers, Critical Reasoning questions require more thought 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than Sentence Correction and Reading Comprehension questions (the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other types of Verbal Ability questions). M oreover, for all but the easiest 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Critical Reasoning questions, you’ll probably need to read the passage and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choices twice before deciding on an answer. So, plan to devote a bit 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 more time to Critical Reasoning questions (at least two minutes per 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 question, on average) than to other Verbal Ability questions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Don’t Second Guess Your Instincts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When in doubt, go with your initial hunch about whether an answer 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choice is viable or not. It’s remarkably easy to over-analyze any Critical 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Reasoning question to the point that you second-guess your own 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 judgment. Although you should carefully consider all five answer choices, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t disregard your instincts. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 356 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level GM AT Critical Reasoning. At this point, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you’ll: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn how to recognize and handle four additional, and more 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 unusual, types of Critical Reasoning questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Learn general strategies for tackling these question types 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere in this N ext Level chapter, you’ll look at four additional question 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 types, each of which involves a quirkier, more specific form of reasoning or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 argument evaluation. Expect at least three of these types on your exam; 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 but don’t expect more than one question of any type. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • H ypothesis questions. For these questions, your task is to recog2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nize a hypothesis that provides a reasonable explanation for a set 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of observations. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Strategy questions. For these questions, your task is to recognize 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an effective course of action based on a set of premises and a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 stated objective. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • N ecessary-inference questions. For these questions, your task is to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinguish, based on a set of premises, valid deductions from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 invalid ones, or to recognize an additional premise needed to 2 12345678901234567890123456789012123456789012345678901 validate a stated conclusion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Parallel-argum ent questions. For these questions, your task is to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recognize similarities in reasoning (that might be flawed) between 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 different arguments. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 357

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Strategy Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In a GM AT strategy question, the passage sets up a scenario where a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decision-maker must develop a plan, or strategy, for solving a “ real-life” 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem such as: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • An undesirable economic or sociological trend 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A decline in a certain business’s revenue or profitability 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • An increasingly serious public-health threat 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Declining performance levels among workers or students 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Typically, the problem at hand is an undesirable trend or development that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the decision-maker hopes to either halt or reverse. The question stem will 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 indicate the decision-maker’s objective. Your task is to identify, among the 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 five answer choices, the strategy or course of action that would be most 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 effective, efficient, or appropriate in achieving the stated objective. Expect 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to encounter no more than one question of this type on the GM AT. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You know you’re dealing with a strategy question when the question stem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 looks similar to one of the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following strategies would be most likely to reverse the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decline in . . .?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ To prevent the continued loss of . . . , it would be best for [decision- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 maker] to” 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ Among the following proposals, which one, if implemented, is likely 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to be most effective in discouraging . . . ?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that each of these question stems contains the word “ most” or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ best.” These are important words. For a strategy question, even the best 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choice will not necessarily achieve the decision-maker’s objective; 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 yet, it will be m ore lik ely to achieve that objective than any other answer 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How to Identify the Best Strategy 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ow do you recognize the “ best” strategy among five choices and 2 2 12345678901234567890123456789012123456789012345678901 distinguish it from less effective, efficient, or appropriate ones? To answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this question for yourself, consider the following GM AT-style passage: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 At Xenon Company, overall worker productivity, which depends 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 primarily on the amount of time workers spend at their workstations, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 has been declining recently. M eanwhile, instead of either bringing 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lunch from home or eating lunch in the company’s cafeteria, an 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 increasing number of Xenon workers have been dining out for lunch, 2 1 2 358 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 which usually takes more time than eating lunch at the Xenon 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 premises. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Given the passage information, ask yourself: H ow w ould I reverse the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decline in w ork er productivity at X enon? Well, based on the passage, you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 know that eating out tends to reduce productivity because it takes more 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 time away from actual work than does eating on the premises. So, to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 increase productivity, it would make sense to implement a plan that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 encourages workers to stay on the premises for lunch or, conversely, that 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 discourages them from going out for lunch. N otice that the general 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strategy here is to encourage workers not just to eat in the cafeteria, and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 not just to bring lunch from home, but, more generally, to remain on 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Xenon premises for lunch. This is an important distinction, as you’re 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about to see! 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When analyzing a GM AT strategy passage, try to think in terms of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 general strategy rather than specific actions. Why? In all likelihood, any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one of a limitless number of specific actions might help in achieving the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 stated goal; so the chances of your conjuring up the one listed as the best 2 12345678901234567890123456789012123456789012345678901 answer choice are rather slim. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow read the following list of possible actions (i.e., answer choices). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Think about each one until you understand why the one listed as the best 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 course of action is more likely to discourage Xenon workers from leaving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Xenon’s premises for lunch than any of the others. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Alternative Courses of Action 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Effective action (potential “best” answ er choice): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Impose stricter limits on the amount of time Xenon’s workers are 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 allowed for lunch breaks. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A ctions that w ould have no clear, direct effect (typical w rong-answ er 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Allow Xenon workers greater flexibility in determining when 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they start and end their workdays. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Establish free after-work nutrition and cooking classes for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Xenon workers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A ctions that could either help or harm , depending on other facts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (typical w rong-answ er choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Replace the vendor that currently provides Xenon’s cafeteria 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 food service with a different one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 359

Take It to the Next Level

Alert!

Chapter 9: Critical Reasoning

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Begin charging workers a fee for parking in Xenon’s employee 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parking lot. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A ctions that w ould help but are too narrow (typical w rong-answ er 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Provide a greater variety of menu choices at the company 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 cafeteria. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Install a kitchenette on the premises for workers to prepare 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 their own lunches. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice the three categories of typical wrong-answer choices. Actions that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 are unlikely to have any direct impact on worker productivity are the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 easiest to recognize as incorrect answers. Actions that might be effective, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 depending on other circumstances, are a bit tougher to recognize as 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect. Finally, actions that clearly help to achieve the objective, but not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to as great an extent as the best choice, are the ones that lure most 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 test-takers away from the correct choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A Typical Strategy Question 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to identify and distinguish between effective and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 less effective strategies, attempt the following GM AT-style strategy 2 2 12345678901234567890123456789012123456789012345678901 question, which is more difficult than average due to the kinds of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wrong-answer choices that follow it. In tackling the question, follow these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 steps: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Before reading the answer choices, try to answer the question, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ What general strategy would help achieve the objective?” If you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 think of a strategy, jot it down. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Scan the answer choices for a specific course of action that would 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 implement that strategy effectively. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. For each other answer choice, ask yourself why it’s less effective 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than the one you selected. (Keep in mind the wrong-answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 categories you just learned about.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 360 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Then, read the analysis of the question and of each answer choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Company Q , a manufacturer of consumer products, offers a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 manufacturer’s rebate through retailers that sell its products. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Retailers offer their own rebate as well on company Q products, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and company Q reimburses the retailer for a portion of each such 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 rebate. Both company Q and its retailers are currently losing money 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on overall sales of company Q products as a result of the rebate 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 scheme. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Which of the following plans, if implemented, is most likely to be 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effective in reversing the losses that company Q and its retailers are 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 currently experiencing from overall sales of company Q products? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Restrict both types of rebates to purchases of products priced 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 only below a certain amount. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Restrict both types of rebates to purchases of certain higher12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 priced products only. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Develop a new advertising campaign designed to boost retail 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sales of company Q ’s newest products. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Reduce the amount of the rebate that retailers offer on 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 purchases of company Q products. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Discontinue reimbursement to retailers for any portion of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rebates on company Q products that retailers pay to consumers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. N otice that the objective is twofold: (1) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decrease company X’s losses and (2) decrease the retailers’ losses. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most effective strategy would help achieve not just one but both objectives. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The manufacturer and retailer currently share the cost of rebates that the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 retailer pays to consumers. Both can reduce their overall costs, thereby 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 reducing losses, by lowering the amount of the retail rebate—as (D) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 provides—and continuing to share the rebate costs. H ence, the course of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 action that (D) suggests is likely to be effective in achieving both stated 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 objectives. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (A) suggests a plan that wouldn’t necessarily reduce losses for 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 either company Q or its retailers. In fact, the plan is just as likely to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 increase those losses. H ow? If company Q and its retailers discontinue 2 12345678901234567890123456789012123456789012345678901 22 rebate offers on certain items, then sales of those items are more likely to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 decline. Since the passage states that it is the rebate items that are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 responsible for current losses, sales of non-rebate items are less likely to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 generate losses, and might even generate profits. A decline in sales of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 profitable items would only add to the overall losses for company X and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 its retailers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 361

Part IV: Verbal A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (B) is incorrect for essentially the same reason as (A). Restricting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the rebate to purchases of only certain items might actually increase losses, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 especially if consumers buy fewer profit-generating (non-rebate) items as a 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 result of the new rebate restrictions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) suggests a plan that is just as likely, if not more likely, to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 increase losses as decrease them. Why? First, the ad campaign will no 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 doubt add to costs. Second, if the ads are effective, there’s no reason to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 believe that consumers enticed by the ads would not take advantage of the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 rebate offers; the more money paid as rebates, the greater the losses for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 company Q and its retailers. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Choice (E) suggests a plan that would obviously help reduce company Q ’s 2 2 12345678901234567890123456789012123456789012345678901 losses, since it would no longer need to reimburse its retailers. By the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 token, however, the plan would increase losses for retailers, who would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now pay the entire rebate. Since the stated objective is to reduce losses not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 just for company Q but also for its retailers, plan (E) is too narrow to be 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the “ best” plan. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In handling basic inference questions like the ones you encountered 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 earlier in the chapter, we suggested that, when in doubt, you should 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choose a narrow conclusion over a broader one. This advice also applies 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to strategy questions—but with a twist. For instance, in answering the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 previous question, (E) suggests a course of action whose effect would be 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 too narrow, which is exactly why (E) is not the best answer! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Strategy Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1. All statements in the passage are premises; so you should assume they 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are all factual. Also, accept the scenario at face value, even though it 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 oversimplifies real life. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Before you read the answer choices, try to formulate an effective 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 general strategy rather than a specific course of action. (O therwise, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you might be frustrated by not finding your proposal listed as an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choice.) Then scan the answer choices for a course of action 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that carries out the strategy. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Remember: Your job is to determine which plan is m ost lik ely to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 achieve the objective, not which one w ill do so. You won’t find any 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bullet-proof plan—one that would work no matter what happens— 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among the answer choices. So don’t waste time looking for one. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Improve your odds of picking the best answer choice by at least 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eliminating the most unlikely ones. Look for choices that “ get it 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 backwards” (that suggest plans that are sure to hurt the cause) or that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 strike you as nonsense (that aren’t directly relevant to the objective). 2 1 2 362 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 9: Critical Reasoning

N ote

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 4. Watch out for proposals that could either help of hinder, depending 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on other circumstances. If there’s a possible “ fip side” to a proposed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 course of action, eliminate it. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Hypothesis Questions 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 In a GM AT hypothesis question, the passage provides two pieces of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 evidence (factual information) that seem inconsistent or in conflict with 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 each other (paradoxical). The passage might involve a “ real-world” 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scenario like one of these: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • An apparent discrepancy between results of different experiments 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or statistical studies 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Two seemingly contrary economic, business, or sociological trends 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Conflicting conclusions drawn by two different individuals based 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the same set of facts 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A surprising difference between two things that are ostensibly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 similar in other ways 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Your task is to recognize a logical explanation (hypothesis) for the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 apparent discrepancy, conflict, or difference. You know you’re dealing 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with a hypothesis question when the question stem looks similar to one of 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following best explains the apparent discrepancy 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between the . . .?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Which of the following, if true, would provide the best explanation 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 for the seemingly contradictory results of the two studies described 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above?” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Each of the following, if true, could help account for the simulta2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 neous increase in . . . and . . . EXCEPT:” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the test-makers use the term hypothesis in describing this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 question type, you’re unlikely to see this actual term in a question stem. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Instead, look for a word such as “ explanation.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 363

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 How to Recognize an Effective Hypothesis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In tackling this question type, the best way to recognize an effective 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hypothesis is to first formulate a broader explanation for the apparent 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 discrepancy or conflict. Let’s do just that, by analyzing three brief 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passages. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Passage 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 W hile on D iet X , m ost dieters reduce their daily calorie intak e from 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 previous levels. H ow ever, people w ho try D iet X generally gain 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rather than lose w eight over the course of the diet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 What might explain the apparent discrepancy between reduced caloric 2 2 12345678901234567890123456789012123456789012345678901 intake and weight gain? O ne good general explanation is that calorie 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 intake is only one of many factors that determine a person’s body weight. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (O ne or two such factors might come to your mind.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Passage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A study com paring the benefits of different popular diets observed 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that dieters tend to lose m ore w eight w hile in D iet Y than w hile on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D iet X . H ow ever, D iet X calls for a low er daily-calorie intak e than 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D iet Y. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What might explain the surprising comparative results of the two diets? 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 O ne general explanation is that Diet X and Diet Y might differ in certain 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other respects—one of which might account for the counter-intuitive 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 results. (O ne or two such respects might come to your mind.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Passage 3 2 12345678901234567890123456789012123456789012345678901 2 O ne independent study on the benefits of dieting observed that 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 people on D iet X lost m ore w eight, on average, than people on D iet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Y. H ow ever, another such study observed just the opposite— that 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 people on D iet X tended to lose less w eight than people on D iet Y. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What might explain the apparent conflict between the results of the two 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 studies? O ne general explanation is that studies often vary in methodol- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ogy, and that different methodologies can yield different results. (O ne or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two possible differences in methodology might come to your mind.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 364 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow examine different hypotheses involving each passage. N otice that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each hypothesis provides a specific scenario rather than a general 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explanation, and that the effective hypotheses support the general 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 explanations we just formulated. Also notice that each poor hypothesis 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 falls into one of these categories (try to determine which category each one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 belongs to): 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • It relies heavily on certain assumed facts. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • It helps explain only one aspect of the discrepancy or conflict. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 • It’s not directly relevant to the discrepancy or conflict. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • It actually makes the discrepancy or conflict m ore inexplicable. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Hypotheses Based on Passage 1 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Effective hypothesis (possible “best” answ er choice): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Diet X makes a person too tired to engage in the kinds of exercise 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that help a person lose weight. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Poor hypotheses (typical w rong-answ er choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • M ost people who try Diet X find it to be bland and lacking in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 variety. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M ost people who try Diet X have already tried other diets but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 failed to lose weight as a result of those diets. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Hypotheses Based on Passage 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Effective hypothesis (possible “best” answ er choice): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dieters find Diet X more restrictive than Diet Y and therefore more 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 difficult to stay on. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Poor hypotheses (typical w rong-answ er choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O ther diets are far more effective than either Diet X or Diet Y. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M ore people on Diet Y than on Diet X are first-time dieters. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Diet X is more effective than Diet Y in satisfying a dieter’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appetite. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Hypotheses Based on Passage 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Effective hypothesis (possible “best” answ er choice): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O ne of the studies observed only first-time dieters, while the other 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 study observed only dieters who had previously lost weight on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other diets. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Poor hypotheses (typical w rong-answ er choices): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Among dieters as a group, Diet X is currently more popular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than Diet Y. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 365

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • N either study continued to observe the dieters’ weight after 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discontinuing the diet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Although lower in calories than Diet Y, Diet X is more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effective in satisfying a dieter’s appetite. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 In a typical hypothesis passage, the number of scenarios that would help 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explain the facts is virtually limitless. So if you happen to conjure up a few 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 good scenarios, keep an open mind. The answer choices may or may not 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 list one of them. That’s why we suggest that, when you try to explain the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 facts for yourself, think in general terms. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A Typical Hypothesis Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In each of the three passages you just analyzed, the discrepancy or conflict 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 was relatively easy to identify and explain. N ow that you’ve seen some 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 easier passages, try tackling a more difficult GM AT-style hypothesis 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question. (What makes this question tricky is that it actually involves tw o 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paradoxes.) As you grapple with it, follow these steps: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Before reading the answer choices, try to formulate a general 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explanation for both paradoxes. Jot down your idea. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Scan the answer choices for a scenario that supports your 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explanation. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. For each other answer choice, ask yourself why it fails to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 adequately explain the paradox. (Keep in mind the wrong-answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 categories you just learned about.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 366 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Then, read the analysis of the question and of each answer choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Kiki birds breed more effectively in some temperatures than in 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 others. During the period from 1991 to 1995, the kiki bird popula2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion in a certain region increased, despite a moratorium, or official 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ban, on the hunting of the kiki bird’s chief predator. During the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 period from 1996 to 2000, the kiki bird population in the same 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 region declined, despite ideal breeding temperatures during that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 period. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following, if true, best explains why the kiki bird 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 population increased during the period from 1991 to 1995, then 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 declined during the period from 1996 to 2000? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. During the period from 1991 to 1995, temperatures in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 region were ideally suited for kiki bird breeding. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. The moratorium on the hunting of the kiki bird’s chief 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 predator was rigorously enforced only after 1995. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. Ideal breeding temperatures for the kiki bird’s chief predator 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 differ from those for the kiki bird. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. The kiki bird is only one of many animal species that is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 potential prey for the bird’s chief predator. 2 12345678901234567890123456789012123456789012345678901 2 E. During the period from 1996 to 2000, the population of the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 kiki bird’s chief predator increased throughout the region. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is B. The passage presents a double-paradox: H ow 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 could the bird’s population increase in the face of an ostensible threat to its 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 survival, then decrease when breeding conditions were ideal? A compre12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 hensive explanation would need to account for both the increase and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 subsequent decrease in population. O ne explanation is that some other 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 condition likely to have an impact on the kiki bird population changed 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from one time period to the other. (B) provides such a condition—a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 specific scenerio that supports this explanation. Without enforcement of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the moratorium, a greater number of the kiki bird’s predators might be 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 killed, which would tend to stabilize and perhaps even result in an increase 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in the kiki bird population. Conversely, enforcing the moratorium would 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 tend to increase the predator’s population, thereby possibly decreasing the 2 12345678901234567890123456789012123456789012345678901 22 bird’s population. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (A) explains why the kiki bird population increased from 1991 to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 1995, but not why the kiki bird population declined from 1996 and 2000. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (C) actually makes the paradox more inexplicable by providing an 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 additional reason why the kiki bird population should have increased 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during the period from 1996 to 2000. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 367

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice(D) is completely irrelevant to the paradox—it serves neither to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explain nor reinforce it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) explains why the kiki bird population decreased from 1996 to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2000, but not why the kiki bird population decreased from 1991 to 1995. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Hypothesis Questions 2 12345678901234567890123456789012123456789012345678901 1. All statements in the passage are premises; so you should assume they 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 are all factual. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Before you read the answer choices, try to formulate a general 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 explanation for the discrepancy or conflict, rather than a specific 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scenario. (O therwise, you might be frustrated by not finding your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scenario listed as an answer choice.) Then scan the answer choices for 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 a scenario that supports your explanation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Remember: Your job is to zero in on an answer choice that helps 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 explain the facts—that provides one possible explanation. N o one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hypothesis is going to cover all the bases; so don’t waste time looking 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for it. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Watch out for the following types of wrong-answer choices: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The incomplete or partial explanation (you’re looking for a choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that helps explain all the facts) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The choice that “ gets it backward” —that makes the discrepancy 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or paradox even more inexplicable 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The choice that assumes too much—that helps explain only if 2 12345678901234567890123456789012123456789012345678901 certain additional facts are assumed 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • The irrelevant scenario (it’s on the topic, but doesn’t relate to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discrepancy or conflict) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Necessary-Inference Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this type of GM AT question, an argument’s conclusion will be 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily inferable (or not inferable) from its premises—in other words, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily true (or false). Expect to encounter at least one necessary12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 inference question on the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT necessary-inference questions come in two varieties. In one type, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the passage provides a series of premises, and your task is to determine 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 which of the five answer choices must be true (or false) based on the 2 2 12345678901234567890123456789012123456789012345678901 premises. You know you’re dealing with this type when the question stem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 looks similar to one of the following: 2 12345678901234567890123456789012123456789012345678901 2 1 2 368 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 9: Critical Reasoning

N ote

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ If the statements above are true, which of the following statements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can logically be derived from them?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following must be true on the basis of the statements 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following can be correctly inferred from the statements 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 above?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ If the statements above are true, any of the following statements 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 might also be true EXCEPT:” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the second type of necessary-inference question, the passage provides 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 one or more premises along with a conclusion, and your task is to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determine what additional premise is required for the conclusion to be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily inferable (true). You know you’re dealing with this type when 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the question stem looks similar to one of the following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The passage’s conclusion is true only if which of the following 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statements is also true?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The conclusion of the argument above cannot be true unless which of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the following is true?” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Any of the following, if introduced into the argument as an 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 additional premise, makes the argument above logically correct 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 EXCEPT:” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice the absence of words such as best, m ost, and least in both groups of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questions above. That’s because, for this type of question, evaluating the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument does not involve a conclusion’s probability but rather its 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 certainty—whether it is true or false, valid or invalid, correct or incorrect, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 inferable or not inferable—based on the premises. So the mode of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reasoning for necessary-inference questions is entirely different than for 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the question types we’ve covered up to this point. If you’re ready to shift to 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 this other mode, read on. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ecessary-inference questions involve deductive reasoning, which is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 actually a specific kind of inference. You’ll see this term used often in the 2 12345678901234567890123456789012123456789012345678901 following pages. A logician might define deduction as the process of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 drawing specific inferences from general laws or propositions. Since the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 definition is a bit technical, the test-makers avoid using any form of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 term in Critical Reasoning questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 369

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Forms and Fallacies of Deductive Reasoning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To master GM AT necessary-inference questions, you need to recognize 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain basic argument forms and fallacies. (A “ fallacy” is simply an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 argument by deduction whose conclusion is incorrect—or whose inference 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is invalid.) The following series of forms are the ones you’re most likely to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 encounter on the GM AT. The best way to identify a form is to first use 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 symbols in premises and conclusions, then analyze an example that 2 2 12345678901234567890123456789012123456789012345678901 matches the form. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Based on the following premise, there is only one valid inference. N otice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the valid inference switches A with B, and negates both. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: If A, then B. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Valid inference: If not B, then not A. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: If B, then A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: If not A, then not B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Example (Argument 1) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Prem ise: If I strike the window with a hammer, the window will 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 break. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: If the window is not broken, then I have not struck 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it with a hammer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: If the window is broken, I have struck it with a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hammer. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: If I do not strike the window with a hammer, the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 window will not break. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (Both invalid inferences overlook that the w indow m ight be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 brok en for any num ber of reasons besides m y having struck it w ith 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a ham m er.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The following argument form and accompanying fallacies are logically 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 identical to the ones above. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: All A are B. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Valid inference: All non-B’s are non-A’s. (N o non-B is an A.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: All B are A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: N o non-A’s are B’s. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 370 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Example (Argument 2) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: All red gremlins are spotted. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Valid inference: N o gremlin that is not spotted is red. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: All spotted gremlins are red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Invalid inference: N o gremlins that are not red are spotted. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (Both invalid inferences overlook that a spotted grem lin m ight be a 2 2 12345678901234567890123456789012123456789012345678901 color other than red.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This next form involves two premises and a third symbol, (C), allowing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inferences (and inviting fallacies) in addition to the ones covered in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 arguments 1 and 2 above. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 3 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: If A, then B. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise: If B, then C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If A, then C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If not C, then not A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Invalid inference: If not A, then not C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Invalid inference: If C, then A. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Example (Argument 3) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: If I strike the window with a hammer, the window will 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 break. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise: If the window is broken, the cold outside air will blow 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 into the house. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: If I strike the window with a hammer, then the cold 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outside air will blow into the house. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If the cold outside air has not blown into the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 house, then I have not struck the window with a hammer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Invalid inference: If I do not strike the window with a hammer, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 window will not break. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Invalid inference: If cold outside air has blown into the house, I 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have struck the window with a hammer. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 371

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The following argument is logically identical to argument 3 above. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 4 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Prem ise: All A are B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: All B are C. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Valid inference: All A are C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: N o non-C is an A. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Invalid inference: N o non-A is a C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: All C are A. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Example (Argument 4) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: All red gremlins are spotted. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Prem ise: All spotted gremlins are female. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (A ssum ption: A gremlin must be either male or female, but not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Valid inference: All red gremlins are female. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: N o male gremlin is red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: N o gremlin that is not red is female. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: All female gremlins are red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In arguments 1–4, each statement is essentially an all-or-none assertion 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (signaled by words such as “ all” and “ no” ). In this next series of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 arguments, the word “ some” is introduced into a premise. For each form, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 try conjuring up your own example (perhaps involving red, spotted, and 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 female gremlins). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 5 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Some A are B. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Valid inference: Some B are A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Invalid inference: Some A are not B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: Some B are not A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (In form al logic the w ord “som e” m eans at least one and possibly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as m any as all; thus the prem ise allow s for the possibility that all A 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 are B, and that all B are A .) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 372 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Argument 6 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Some A are B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Prem ise: Some B are C. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: Some B are A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Valid inference: Some C are B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: Some A are C. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Invalid inference: Some C are A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (If a B is an A , it is not necessarily a C as w ell; in other w ords, the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 set of B’s that are also A ’s does not necessarily overlap the set B’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that are also C’s.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument 7 2 12345678901234567890123456789012123456789012345678901 Prem ise: Some A are B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise: All B are C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: Some B are A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: Some A are C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: Some C are A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Invalid inference: All C are B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Invalid inference: All C are A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The following two arguments involve “ either-or” forms: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Argument 8 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Either A or B, but not both. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If A, then not B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If B, then not A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If not B, then A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If not A, then B. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Argument 9 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Either A or B, but not both. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: Either B or C, but not both. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If B, then not C (and not A). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Valid inference: If A, then C (but not B). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Valid inference: If C, then A (but not B). 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 373

Part IV: Verbal A bility

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X-Ref

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A Typical Necessary-Inference Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow that you know how to recognize various forms of deductive 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning and distinguish between valid and invalid inferences, attempt 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the following GM AT-style question, which is a bit more difficult than 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 average for this question type. As you tackle the question, follow these 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 steps: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Try to reduce the passage to simple statements using symbols 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (letters). Jot down the premise and conclusion using those 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 symbols. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Before reading the answer choices, try to determine the missing 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 premise for yourself. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Scan the answer choices for your answer. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. For each answer choice you eliminated, try to determine what 2 2 12345678901234567890123456789012123456789012345678901 valid conclusion (if any) would be inferable by adding the premise 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provided in the answer choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Then, read the analysis of the question and of each answer choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N otice that this question provides the conclusion, then asks about the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessary premise that’s missing; it’s an example of one of the two basic 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 types of necessary-inference questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In the country of Xania, periods of political instability are always 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accompanied by a volatile Xania stock market and by volatility of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Xania’s currency compared to currencies of other countries. At the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 present time, Xania’s currency is experiencing volatility. H ence, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Xania stock market must also be experiencing volatility. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Which of the following allows the conclusion above to be properly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 drawn? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. Whenever Xania is politically stable, the Xania currency is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stable as well. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. Whenever the Xania currency is stable, Xania is politically 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stable as well. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Whenever the Xania stock market is unstable, Xania is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 politically unstable as well. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Whenever the Xania stock market is unstable, the Xania 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 currency is unstable as well. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 E. Whenever the Xania stock market is stable, the Xania currency 2 2 12345678901234567890123456789012123456789012345678901 2 1 is stable as well. 2 374 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. The argument boils down to the following: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise 1: If there is political instability, then the stock market is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 volatile (unstable). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise 2: If there is political instability, then the currency is volatile 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (unstable). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise 3: The currency is volatile (unstable). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: The stock market is volatile (unstable). 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To reveal the argument’s structure, let’s reduce it to symbols: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Prem ise 1: If A, then B. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise 2: If A, then C. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise 3: C. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Conclusion: B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The conclusion above requires the following additional premise: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise 4: If the currency is volatile (unstable), then there is political 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 instability. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise 4: If C, then A. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O nly answer choice (A) provides this essential premise. N ote that premise 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 number 4 above is essentially the same proposition as answer choice (A). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In other words, the following two propositions are logically identical: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise 4: If C, then A. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A nsw er choice (A ): If not A, then not C. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (B) merely reiterates premise number 2. In other words, the 2 12345678901234567890123456789012123456789012345678901 following two statements are essentially the same: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If X, then Y. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If not Y, then not X. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (C) commits the following fallacy: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Prem ise: If X, then Y. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: If Y, then X. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) would lead to the conclusion that if the stock market is volatile 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (unstable), then the currency is volatile (unstable). In other words, (D) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 commits the same fallacy as (C): 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: If X, then Y. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 Conclusion: If Y, then X. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 375

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (E) merely reiterates the argument’s conclusion. In other words, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following two statements are essentially the same: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 If X, then Y. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If not Y, then not X. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Necessary-Inference Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. If the question asks for a missing premise, identify the premise(s) and 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 conclusion in the passage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. If you’re having trouble following the logic, reduce each part of the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 passage to simple statements using letters as symbols. Write down the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 form of the argument on paper. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Pre-phrase the answer to the question by determining the additional 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 premise needed for the conclusion to be valid (or the conclusion that 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 necessarily follows from the stated premises). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Express your answer using symbols. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. If you’re having trouble making sense of a particular statement in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage, try to rephrase it so its logical meaning is clearer. Eliminating 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 double-negatives can be particularly helpful. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Confusing: O nly gremlins that are spotted are red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Clear: All red gremlins are spotted. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Confusing: If a gremlin is not spotted, then it cannot be red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Confusing: A gremlin is spotted only if it is red. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Clear: If a gremlin is red, then it must be spotted. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 6. Look out for the following types of wrong answers: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A statement that results in one of the logical fallacies identified 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in this chapter. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A statement that merely reiterates a stated premise (or stated 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conclusion), expressing it in a slightly different way. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Parallel-Argument Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this type of question, the passage and the five answer choices each 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provide an argument (one or more premises and a conclusion). Your task is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to determine which of the five choices provides the argument most similar 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in its pattern of reasoning to the pattern in the passage. Don’t expect to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 encounter more than one question of this type on the GM AT. 2 1 2 376 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 You know you’re dealing with a parallel-argument question when the ques- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion stem looks similar to one of the following (notice that the first two are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essentially the same, but the third one suggests a slightly different task): 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 “ Which of the following is most like the argument above in its logical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 structure?” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 “ Which of the following illustrates a pattern of reasoning most similar 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the pattern of reasoning in the argument above?” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 “ The flawed reasoning in the argument above is most similar to the 2 2 12345678901234567890123456789012123456789012345678901 2 reasoning in which of the following arguments?” 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Parallel-argument questions almost always involve deductive reasoning. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To handle these questions, you apply the forms and fallacies you just 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 learned to the unique parallel-argument format. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A Typical Parallel-Argument Question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Attempt the following GM AT-style parallel-argument question, which is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 average in difficulty. As you tackle the question, follow these steps: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. Try to reduce the passage to simple statements using symbols (let- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ters). Jot down the premise and conclusion using these symbols. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Perform the same task (step 1) for each answer choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Compare the pattern of reasoning in each answer choice to the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 pattern in the original passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Then, read the analysis of the question and of each answer choice. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 377

Take It to the Next Level

Tip

Chapter 9: Critical Reasoning

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Very few software engineers have left M icroFirm Corporation to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 seek employment elsewhere. Thus, unless CompTech Corporation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 increases the salaries of its software engineers to the same level as 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 those of M icroFirm, these CompTech employees are likely to leave 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 CompTech for another employer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 The flawed reasoning in the argument above is most similar to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning in which of the following arguments? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Robert does not gamble, and he has never been penniless. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Therefore, if Gina refrains from gambling she will also avoid 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 being penniless. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. If Dan throws a baseball directly at the window, the window 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pane will surely break. The window pane is not broken, so 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dan has not thrown a baseball directly at it. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. If a piano sits in a humid room the piano will need tuning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 within a week. This piano needs tuning. Therefore, it must 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 have sat in a humid room for at least a week. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Diligent practice results in perfection. H ence, one must practice 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 diligently in order to achieve perfection. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. M ore expensive cars are stolen than inexpensive cars. Accord12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 ingly, owners of expensive cars should carry auto theft 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 insurance, whereas owners of inexpensive cars should not. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The original argument’s line of reasoning is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 essentially as follows: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: The well-paid engineers at M icroFirm do not quit their jobs. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Conclusion: If CompTech engineers are not well-paid, they will quit 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 their jobs. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To reveal the argument’s logical structure, let’s express it using letters as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 symbols: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Prem ise: All A’s are B’s. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Conclusion: If not A, then not B. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The reasoning is fallacious (flawed), because it fails to account for other 2 2 12345678901234567890123456789012123456789012345678901 possible reasons why M icroFirm engineers have not left their jobs. (Some 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B’s might not be A’s.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is the only answer choice the demonstrates the same essential 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pattern of flawed reasoning. To recognize the similarity we can rephrase 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the argument’s sentence structure to match the essence of the original 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 argument: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Prem ise: All people who practice diligently (A) achieve perfection (B). 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 378 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 9: Critical Reasoning

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Conclusion: If one does not practice diligently (not A) one cannot 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 achieve perfection (not B). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) reasons essentially as follows: O ne certain A is B. Therefore, if 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A then B. This reasoning is flawed, but in a different respect than the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reasoning in the original argument. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Choice (B) reasons essentially as follows: If A, then B. N ot B. Therefore, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not A. This reasoning is sound (not flawed). 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Choice (C) reasons essentially as follows: If A, then B. Therefore, if B, then 2 2 12345678901234567890123456789012123456789012345678901 A. This reasoning is flawed, but in a different respect than the reasoning in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the original argument. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) does not involve deductive reasoning and can’t easily be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expressed in symbols. Without additional evidence, it’s impossible to 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 determine the strength of the argument. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Tips for Tackling Parallel-Argument Questions 2 12345678901234567890123456789012123456789012345678901 1. Before reading the answer choices, reduce the original passage to its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basic structure. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. Express the argument in general terms—perhaps using letters as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 symbols—that incorporate the argument’s logic but not its subject 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 matter. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. Don’t equate logical structure with sequence. The passage might 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 provide the conclusion first, while the best answer choice provides its 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 conclusion last (or vice-versa). In other words, try to identify parallel 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 logic—not parallel sequence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. Don’t equate logical structure with subject matter. Be suspicious of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any answer choice involving a topic that is similar to that of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage. Although that answer choice m ight be the best one, more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than likely it is not. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 379

Chapter

10 Sentence Correction 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to GM AT Sentence Correction. At this point, you’ll: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn a step-by-step approach to handling any Sentence Correc2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion question 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn to recognize and fix basic grammatical errors and problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with sentence structure and verbosity 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn success keys for tackling GM AT Sentence Correction 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence Correction—Your 4-Step Game Plan 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The first task in this chapter is to learn the four basic steps for handling a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Sentence Correction question. You’ll apply these steps to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following sample question: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Despite sophisticated computer models for assessing risk, such a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 model is nevertheless limited in their ability to define what risk is. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. Despite sophisticated computer models for assessing risk, such 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a model is nevertheless 2 12345678901234567890123456789012123456789012345678901 B. Sophisticated computer models, which assess risk, are never12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 theless 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Despite their sophistication, computer models for assessing 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 risk are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Assessment of risk can be achieved with sophisticated com12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 puter models, but these models are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Assessing risk with sophisticated computer models is limited 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 because such models are 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 380

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 1: Read the original sentence carefully. As you do so, ask yourself: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Does it sound odd or wrong to my ear? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Do any errors in grammar jump out at me? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Is the sentence confusing, and would I have to read it again to try 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 and figure out what it means? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If your answer to any of these questions is “ yes,” you can confidently 2 2 12345678901234567890123456789012123456789012345678901 eliminate choice (A), the original underlined part, even if you’re not sure 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 why it’s wrong. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Plug your remaining choices, one at a time, into the original 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 sentence, and read the entire revised sentence. As you do so, ask yourself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the same three questions as in Step 1, and eliminate any choice for which 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your answer to any of those questions is “ yes.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 3: If you still haven’t narrowed the choices down to a clear winner, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 compare the remaining candidates. Resolve close judgment calls in favor of: 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A briefer, more concise version 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A version that more accurately conveys the intended meaning of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the sentence 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A less awkward version 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 4: Verify your selection before confirming your response. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Check your selection one more time by plugging it into the sentence. If it 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sounds right, confirm your response, and move on. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ow let’s walk through the sample question about computer models, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using this 4-step approach. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 1: Upon a first reading, doesn’t “ such a model” sound a bit 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 awkward? That’s a good clue that (A) is not the correct response. In fact, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the original sentence contains two flaws. O ne is a grammatical error: the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 plural pronoun their is used to refer to the singular noun m odel. Either 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 both should be plural or both should be singular, but they must match! 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The word their in not part of the underlined phrase, so look for an answer 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 choice that uses m odels instead of m odel. (In grammatical terminology, the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 original sentence contains an error in “ pronoun-antecedent agreement.” ) 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The other flaw is one of ineffective expression: the first clause (before the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 comma) is structured differently than the second clause, and the result is 2 2 12345678901234567890123456789012123456789012345678901 an awkward and confusing sentence. So you should look for an answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice that renders the sentence clearer and perhaps a bit more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise—one that helps the sentence sound a bit sweeter and “ flow” more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 smoothly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 381

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 2: Substitute each answer choice in turn for the underlined 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 part.Choice (B) does not contain any grammatical errors. But doesn’t the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrase w hich assess risk appear to describe computer models in general 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 rather than models for assessing risk? Surely, this isn’t the intended 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 meaning of the sentence. (B) is a perfect example of an answer choice that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is wrong because it either distorts, confuses, or obscures the intended 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 meaning of the sentence. Eliminate (B). Choice (C) takes care of both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems with the original sentence. The plural noun m odels matches the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 plural pronoun their, and both clauses are now constructed in a similar 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 way, making for a clearer and briefer sentence. (C) is probably the correct 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer, but read the remaining choices anyway. Choice (D) sounds pretty 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 good when you read it as part of the sentence, doesn’t it? N o grammatical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 errors jump out at you. So is it a toss-up between (C) and (D)? Well, go on 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to (E) for now, then come back to the (C)-versus-(D) debate. Choice (E) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 incorrectly uses the phrase is lim ited to describe assessing risk . It is the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 computer models’ ability, not assessing risk, that is limited. Eliminate (E). 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t select an answer choice as the correct one just because it fixes every 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 flaw in the original sentence. If (A) is flawed, you can be certain that one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or two of the answer choices will fix the flaw, but create a new flaw! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: Go back to (C) and (D). Is one less awkward than the other? M ore 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise? Closer in meaning to the original version? Perhaps you noticed 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the first clause in (D) (assessm ent of risk can be achieved) sounds a bit 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awkward. So you’ve got a good reason to choose (C) over (D). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Check (C) one more time by plugging it into the sentence: D espite 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 their sophistication, com puter m odels for assessing risk are lim ited in their 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ability to define w hat risk is. Sounds great! Confirm your response, and 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 move on to the next question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Grammatical Errors Involving Parts of Speech 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In the remainder of this chapter, you’ll examine basic kinds of grammatical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 errors and problems with sentence structure and written expression. These 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are the ones that, for most test-takers, are easiest to recognize and most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 straightforward to fix. In addition to learning how to fix these problems, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll see how the GM AT might test you on each one. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 382 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Tip

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 We’ll start with grammatical errors involving parts of speech—which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 include adjectives, adverbs, pronouns, and verbs. H ere are the kinds of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 errors we’ll cover in the pages ahead: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Error in choice between adjective and adverb 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Error in choice of adjective for comparisons 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Error in choice of personal pronoun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Error in pronoun-antecedent agreement 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Error in subject-verb agreement 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 By the way, immersing yourself in the rules of English grammar and the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 guidelines for effective written expression (as you’re about to do) will 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 help you not only for Sentence Correction questions but also for the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Analytical Writing Assessment (AWA) sections of the GM AT. So pay close 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 attention; your efforts here will be doubly rewarded on exam day! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Error in Choice Between Adjective and Adverb 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A djectives describe nouns, while adverbs describe verbs, adjectives, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other adverbs. Adverbs generally end with -ly, while adjectives don’t. Look 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for adjectives incorrectly used as adverbs (and vice versa). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: The movie ended sudden. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: The movie ended suddenly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (The adverb suddenly describes the verb ended.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although adverbs generally end with -ly, some adverbs don’t. Also, if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re dealing with two adverbs in a row, sometimes the -ly is dropped 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from the second adverb. There are no hard-and-fast rules here. Trust your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ear as to what sounds correct. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: Risk-takers drive fastly, play hardly, and arrive lately for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their appointments. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Risk-takers drive fast, play hard, and arrive late for their 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appointments. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: The Canadian skater jumps particularly highly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: The Canadian skater jumps particularly high. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 383

Part IV: Verbal A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Also keep in mind that adjectives, not adverbs, should be used to describe 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 verbs involving the senses (sight, taste, smell, hearing, touch). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: Dinner tasted deliciously. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: Dinner tasted aw ful delicious. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 correct: Dinner tasted aw fully delicious. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (The adjective delicious is used to describe the verb tasted, while the 2 2 12345678901234567890123456789012123456789012345678901 adverb aw fully is used to describe delicious.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow look at how the test-makers might try to slip one of these errors past 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you in a GM AT sentence. In the question below, the original sentence is 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 flawed, so (A) is correct. Your choice is between (C) and (D). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To help you focus on the specific grammatical error at hand, we’ll 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simplify the Sentence Correction format by listing just three answer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choices, and by limiting the kinds of errors to one or two. Actual GM AT 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions include five answer choices, of course. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A recent report from the Department of Energy suggests that over 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the next two decades demand for crude oil will increase at an 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 alarming fast rate, and greatly exceeds most economists’ previous 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forecasts. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. increase at an alarming fast rate, and greatly exceeds 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. *** 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. increase at an alarmingly fast rate, greatly exceeding 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. be at an increasingly alarming rate and will greatly exceed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The original sentence incorrectly uses the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adjective alarm ing instead of the adverb alarm ingly to describe the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adjective fast. The original sentence also contains an additional, and more 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 conspicuous, flaw. The phrase and greatly ex ceeds improperly suggests 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the rate is increasing alarmingly at the present time. H owever, the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence as a whole makes clear that this is a future event. (C) corrects 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 both of these problems. Although (D) also corrects both problems, it 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 creates a new flaw. The use of the word be to refer to dem and is an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 awkward and inappropriate expression of the idea which the sentence 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 attempts to convey. Be suggests one point in time, but the sentence intends 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to describe the changing demand over a period of time. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 384 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Alert!

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Because this sort of error is generally easy to spot in a sentence, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT test-makers will probably try to sneak it past you by including 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 another (and possibly more conspicuous) flaw as well, in the hope that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll carelessly overlook the incorrect adjective or adverb. Beat them at 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their own game by looking carefully at adjectives and adverbs, especially 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 w hen they appear in pairs (as in the sample question above)! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Error in Choice of Adjective for Comparisons 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you read a GM AT sentence, pay close attention to any adjective ending 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in -er, -ier, -est, and -iest. Adjectives ending in -er and -ier should be used to 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 compare tw o things, while adjectives ending in -est and -iest should be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 used when dealing with three or more things. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Comparative form Superlative form 2 12345678901234567890123456789012123456789012345678901 (two things) (three or more things) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 brightest brighter 12345678901234567890123456789012123456789012345678901 22 greatest greater 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fewest fewer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 least lesser 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most more 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 best better 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: Frank is less intelligent than the other four students. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Frank is the least intelligent among the five students. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Frank is less intelligent than any of the other four students 2 12345678901234567890123456789012123456789012345678901 (The word any is singular, so the comparative form is proper.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Another way of making a comparison is to precede the adjective with a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 word such as m ore, less, m ost, or least. But if both methods are used 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 together, the sentence is incorrect. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: Francis is m ore healthier than Greg. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Francis is healthier than Greg. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 385

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence involving the kinds of issues we just 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 covered. The original version (A) is faulty, so your choice is between the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The more busier the trading floor at the stock exchange, the less 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opportunities large institutional investors have to influence the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 direction of price by initiating large leveraged transactions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. The more busier the trading floor at the stock exchange, the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 less opportunities 2 12345678901234567890123456789012123456789012345678901 2 B. *** 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. The busier trading floor at the stock exchange results in less 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opportunities 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The busier the trading floor at the stock exchange, the fewer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opportunities 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. In the original sentence, the phrase m ore busier 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrectly uses both comparative methods. (E) corrects this flaw by using 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 busier. The original sentence includes another flaw as well. The phrase less 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opportunities is incorrect; the word few er should be used instead of less in 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 referring to numbers of things—as opposed to the amount of one thing. (E) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corrects this flaw. H owever, (D) does not. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Error in Choice of Personal Pronoun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Personal pronouns are words such as they, m e, his, and itself—words that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 refer to specific people, places, and things. Pronouns take different forms, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 called “ cases,” depending on how they are used in a sentence. Just for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 record, you’ll find all the various cases in the following table. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Objective 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Case Subjective Possessive Objective 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 —Reflexive Case Case Case 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first-person I my, mine me myself 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 singular 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 first-person we our, ours us ourselves 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 second-person you your, you yourself 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 singular yours 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 second-person you your, you yourselves 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural yours 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 386 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Alert!

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Objective 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Case Subjective Possessive Objective 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 —Reflexive Case Case Case 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 third-person he, she, his, her, him, himself, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 singular it hers, its her, it herself, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 itself 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 third-person they their, them themselves 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 plural theirs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You can generally trust your ear when it comes to detecting personal2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 pronoun errors. In some cases, however, your ear can betray you, so make 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sure you are “ tuned in” to the following uses of pronouns. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: Either him or Trevor w ould be the best spokesman for our 2 12345678901234567890123456789012123456789012345678901 group. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: The best spokesperson for our group w ould be either him or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Trevor. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Either Trevor or he w ould be the best spokesperson for our 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 group. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: The best spokesperson for our group w ould be either he or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Trevor. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (Any form of the verb to be is followed by a subject pronoun, such 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as he.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: O ne can’t help admiring them cooperating with one another. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: O ne can’t help admiring their cooperating with one another. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (The possessive form is used when the pronoun is part of a “ noun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clause,” such as their cooperating.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: In striving to understand others, we also learn more about us. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: In striving to understand others, w e also learn more about 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ourselves. (A reflex ive pronoun is used to refer to the sentence’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subject.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What appears to be a reflexive pronoun may not even be a real word! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a list of “ non-words,” any of which might masquerade as a 2 12345678901234567890123456789012123456789012345678901 reflexive pronoun in a GM AT sentence: ourself, our ow n selves, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 theirselves, theirself, them self, their ow n self, and their ow n selves. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 387

Part IV: Verbal A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence involving the issue of pronoun case. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Those of the legislators opposing the swampland protection bill 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have only theirselves to blame for the plight of the endangered 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 black thrush bird. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. of the legislators opposing the swampland protection bill have 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 only theirselves 2 12345678901234567890123456789012123456789012345678901 2 B. *** 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Those legislators, who opposed the swampland protection bill, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 have only themselves to blame 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Those legislators who opposed the swampland protection bill 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have only themselves to blame 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. The original sentence suffers from two flaws. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 First, theirselves is a non-word and should be replaced with the reflexive 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pronoun them selves. Second, the phrase those of the legislators opposing, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 while not grammatically incorrect, is awkward and confusing. (D) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 provides a briefer and clearer alternative phrase and corrects the pronoun 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 error. (C) also corrects the pronoun error, but creates a new problem by 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 setting off a portion of the sentence with commas. In doing so, (C) infers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that all of “ those legislators” are opposed the bill, thereby distorting the 2 2 12345678901234567890123456789012123456789012345678901 2 intended meaning of the original sentence. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In GM AT sentences, you’ll find very few (if any) first-person or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 second-person personal pronouns. Why do the test-makers shun pro- 2 2 12345678901234567890123456789012123456789012345678901 nouns such as w e, you, and our? Because GM AT sentences are academic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in nature, not conversational or informal. (But you probably already 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 noticed that, didn’t you?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Error in Pronoun-Antecedent Agreement 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 An antecedent is simply the noun to which a pronoun refers. In GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentences, make sure that pronouns agree in num ber (singular or plural) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with their antecedents. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 singular: Studying other artists actually helps a young painter develop 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 his or her own style. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural: Studying other artists actually helps young painters develop 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their own style. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 388 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 But what’s the rule for pronouns that refer to nouns describing a group of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 people or things (called collective nouns)? The same rule applies here as for 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subject-verb agreement: the pronoun can either be singular or plural, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 depending on whether the collective noun is used in a singular or plural 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 correct: The legislature hesitates to punish its own members for ethics 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 violations. (L egislature used in the singular sense.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 correct: The planning com m ittee recessed, but Jack continued to work 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 without them .(Com m ittee used in the plural sense.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Singular pronouns are generally used in referring to antecedents such as 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 each, either, neither, and one. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: N either of the two countries imposes an income tax on 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 its citizens. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: O ne cannot be too kind to oneself. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 When it comes to antecedents such as anyone, anybody, everybody, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 everyone, or a person, the rules of English grammar get a bit fuzzy. For 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 instance, any grammarian would agree that the first sentence below is 2 12345678901234567890123456789012123456789012345678901 correct, but whether the second one is correct is hotly debated among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 grammarians. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: If anyone offends you, please don’t confront him or her. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 proper? If anyone offends you, please don’t confront them . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Because the rule of grammar here is unsettled, rest assured that you will 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not encounter these words as pronoun antecedents on the GM AT. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence involving pronoun-antecedent 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 agreement. The original version (A) is faulty, so your choice is between the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two alternative versions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 389

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 M any powerful leaders throughout history, such as President N ixon 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 during the Watergate debacle, had become victimized by his own 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paranoia. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. M any powerful leaders throughout history, such as President 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ixon during the Watergate debacle, had become victimized by 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 his own paranoia. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. M any powerful leaders throughout history, such as President 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ixon during the Watergate debacle, have become victims of 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 their own paranoia. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Throughout history, many a powerful leader, such as President 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 N ixon during the Watergate debacle, have by his or her own 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paranoia become a victim. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. *** 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. The original sentence intends to make the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 point that m any leaders (plural) have (plural verb) become victimized by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 their (plural pronoun) own paranoia. H owever, by using the singular had 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and his, the final clause seems to refer to N ix on instead of to leaders. (B) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correctly uses the plurals have and their. In (C), the plural subject leaders 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 has been transformed into a singular subject (m any a pow erful leader). 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 This form is grammatically acceptable. H owever, the subject’s verb, as well 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as any pronouns that refer to the subject, should now be singular as well. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the singular his or her is correct, the plural verb have is incorrect. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So (C) contains a subject-verb agreement error. (C) also improperly 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 separates the words have and becom e. The phrase have becom e is an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 example of an “ infinitive” verb form. H ave you ever heard the phrase 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ split infinitive” ? (C) provides a good example of one; and it’s 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 grammatically incorrect. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Error in Subject-Verb Agreement 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A verb should always “ agree” in number—either singular or plural—with 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 its subject. A singular subject takes a singular verb, while a plural subject 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 takes a plural verb. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct (singular): The parade w as spectacular. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct (singular): Both parades w ere spectacular. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct (plural): The parade and the pageant w ere spectacular. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 390 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t be fooled by any words or phrases that might separate the verb from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 its subject. In each sentence below, the singular verb w as agrees with its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subject, the singular noun parade. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 correct: The parade of cars w as spectacular. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: The parade of cars and horses w as spectacular. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 An intervening clause set off by commas can serve an especially effective 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ smokescreen” for a subject-verb agreement error. Pay careful attention to 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 what comes immediately before and after the intervening clause. Reading 2 2 12345678901234567890123456789012123456789012345678901 the sentence without the clause often reveal a subject-verb agreement error. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: John, as well as his sister, w ere absent from school yesterday. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: John, as well as his sister, w as absent from school yesterday. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere’s a GM AT-style sentence that raises a subject-verb agreement issue. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Grade school instruction in ethical and social values, particularly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the values of respect and of tolerance, are required for any democ2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 racy to thrive. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. values of respect and of tolerance, are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. value of respect, together with tolerance, is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. values of respect and tolerance, is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is (C). In the original sentence, the subject of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural verb are is the singular noun instruction. The correct answer choice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 must correct this subject-verb agreement problem. Also, the second of in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the underlined phrase should be deleted because its use results in an 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 awkward and nonsensical clause, which seems to suggest that of tolerance 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is a value. Both (B) and (C) correct the problem by changing are to is and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by dropping the second of. H owever, (B) creates two new problems. First, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 using the word value instead of values distorts the meaning of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 underlined phrase. Respect and tolerance are not referred to in (B) as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 values. H owever, the original sentence, considered as a whole, clearly 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 intends to refer to respect and tolerance as examples of ethical and social 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 values. Secondly, the phrase together w ith tolerance (set off by commas), 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 adds an unnecessary clause and results in a sentence that is wordy and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 awkward. (C) is clearer and more concise. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 391

Part IV: Verbal A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep a keen eye out for GM AT sentences that separate verbs from their 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subjects. In every one of these sentences, it’s a sure bet that the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 test-makers are testing you on subject-verb agreement. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Problems Involving a Sentence’s Structural 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Elements 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, let’s move ahead to another broad area covered in GM AT Sentence 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Correction: sentence structure. H ere are the specific kinds of structural 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems we’ll cover in this section: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • Sentence fragments (incomplete sentences) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Two main clauses connected improperly 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Faulty parallelism involving lists, or “ strings” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Faulty parallelism involving correlatives 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Sentence Fragments (Incomplete Sentences) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It was probably your fifth- or sixth-grade teacher who first informed you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that a sentence must include both a subject and a predicate. Well, your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 teacher was right, and the GM AT is here to remind you. Grammarians call 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incomplete sentences “ sentence fragments.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fragment: Expensive private colleges, generally out of financial reach 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for most families with college-aged children. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fragment: Without question, responsibility for building and maintain- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ing safe bridges. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, you probably won’t have any trouble recognizing a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence fragment. H owever, an especially long fragment might escape 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your detection if you’re not paying close attention. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 392 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Tip

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style example of a sentence fragment. The original 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 version (A) is faulty, so your choice is between the two alternative versions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O ne cannot deny that, even after the initial flurry of the feminist 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 movement subsided, Congresswoman Bella Abzug, undeniably her 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 female constituency’s truest voice, as well as its most public 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 advocate. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. as well as its most public advocate 2 12345678901234567890123456789012123456789012345678901 2 B. who was her constituency’s most public advocate 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. was also its most public advocate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. If you use (D), the sentence can be distilled 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 down to this: O ne cannot deny that Bella A bzug w as its [the fem inist 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 m ovem ent’s] m ost public advocate. Adding the verb w as is the key to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 transforming the original fragment into a complete sentence. N either (A) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 nor (C) provides the verb needed for a complete sentence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you’re not sure whether it’s a complete sentence, ask yourself two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions: (1) What’s the subject? and (2) Where’s the verb that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 establishes a predicate? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Two Main Clauses Connected Improperly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A m ain clause is any clause that can stand alone as a complete sentence. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 There’s nothing wrong with combining two main clauses into one 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence—as long as the clauses are properly connected. O n the GM AT, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 look for any of these three flaws: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • N o punctuation between main clauses 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A comma between main clauses, but no connecting word (such as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and, or, but, yet, for, so). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A confusing or inappropriate connecting word 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dan ran out of luck M ike continued to win. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dan ran out of luck, M ike continued to win. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Dan ran out of luck, or M ike continued to win. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 393

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dan ran out of luck, but M ike continued to win. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Dan ran out of luck, w hile M ike continued to win. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Dan ran out of luck, yet M ike continued to win. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 H ere’s a GM AT-style sentence that focuses on the comma-splice issue. The 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 versions listed here. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Aleutian Islands of Alaska include many islands near the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mainland, the majority of them are uninhabited by humans. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. the majority of them are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. *** 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. so the majority of them are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. yet the majority of them are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. N otice that (E) includes a connecting word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (yet) that gives the sentence a reasonable meaning by underscoring the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contrast between the mainland (which is populated) and the unpopulated 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nearby islands. Although (C) adds a connecting word (so), this word is 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 inappropriate—inferring that the islands are unpopulated because they are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 near the mainland. The resulting sentence is nonsensical, so (C) can’t be 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the best answer choice. (By the way, notice the appropriate use of so as a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 connector in the preceding sentence!) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Faulty Parallelism Involving a List or “String” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Sentence elements that are grammatically equal should be constructed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 similarly; otherwise the result will be what is referred to as faulty 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 parallelism . For instance, whenever you see a list, or “ string,” of items in a 2 2 12345678901234567890123456789012123456789012345678901 sentence, look for inconsistent or mixed use of: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Prepositions (such as in, w ith, or on) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Gerunds (verbs with an -ing added to the end) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Infinitives (plural verb preceded by to) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Articles (such as a and the) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 faulty: Flight 82 travels first to Boise, then to Denver, then Salt Lake 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 City. (To precedes only the first two of the three cities in this list.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parallel: Flight 82 travels first to Boise, then Denver, then Salt Lake 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 City. 2 12345678901234567890123456789012123456789012345678901 2 1 2 394 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 parallel: Flight 82 travels first to Boise, then to Denver, then to Salt 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lake City. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 faulty: Being understaffed, lack of funding, and being outpaced by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 competitors soon resulted in the fledgling company’s going out of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 business. (O nly two of the three listed items begin with the gerund 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 being.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 parallel: Understaffed, underfunded, and outpaced by competitors, the 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 fledgling company soon went out of business. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parallel: As a result of understaffing, insufficient funding, and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 outpacing on the part of its competitors, the fledgling company soon 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 went out of business. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 faulty: Among the mountains, the sea and desert, we humans have yet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to fully explore only the sea. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 parallel: Among the mountains, sea and desert, we humans have yet to 2 12345678901234567890123456789012123456789012345678901 fully explore only the sea. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 parallel: Among the mountains, the sea and the desert, we humans 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have yet to fully explore only the sea. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence involving lists and faulty parallelism. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Long before the abolition of slavery, many freed indentured 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 servants were able to acquire property, to interact with people of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 other races, and maintain their freedom. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. to interact with people of other races and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. interact with people of other races, and maintain 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. to interact with people of other races, as well as maintaining 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. N otice the string of three items in this sentence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 In the original version, the second item repeats the preposition to, but the 2 12345678901234567890123456789012123456789012345678901 22 third item does not. (B) corrects this faulty parallelism. (D) improperly 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mixes the use of a prepositional phrase (beginning with to) with a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 construction that uses a gerund (m aintaining) instead. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 395

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Just because all items in a string are parallel, don’t assume that the string 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is problem-free! Repeating the same preposition, article, or other modifier 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 before each item in a string can sometimes result in an awkward and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unnecessarily wordy sentence. In other instances, repeating the modifier 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 may be necessary to achieve clarity. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 awkward: Some pachyderms can go for days at a time without water 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or without food or without sleep. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 better: Some pachyderms can go for days at a time without water, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 food, or sleep. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unclear: Going for broke and broke usually carry identical conse- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quences. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 clear: Going for broke and going broke usually carry identical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 consequences. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Faulty Parallelism Involving Correlatives 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 You just saw how items in a list can suffer from faulty parallelism. N ow 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 look at how this grammatical error shows up in what are called 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correlatives. H ere are the most commonly used correlatives: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • either . . . or . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • neither . . . nor . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • both . . . and . . . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • not only . . . but also . . . 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Whenever you spot a correlative in a sentence, make sure that the element 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 immediately following the first correlative term is parallel in construction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to the element following the second term. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 faulty: Those wishing to participate should either contact us by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 telephone or should send e-mail to us. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parallel (but repetitive): Those wishing to participate either should 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contact us by telephone or should send e-mail to us. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 parallel: Those wishing to participate should either contact us by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 telephone or send e-mail to us. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 396 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at how faulty parallelism in a correlative might appear in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT sentence. The original version (A) is faulty, so your choice is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between the two alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Species diversity in the Amazon basin results not from climate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stability, as once believed, but climate disturbances. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. from climate stability, as once believed, but 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. only from climate stability, as once believed, but instead from 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. *** 2 12345678901234567890123456789012123456789012345678901 2 D. *** 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. from climate stability, as once believed, but rather from 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is (E). As it stands, the original sentence might carry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one of two very different meanings: (1) stability and disturbances both 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 contribute to species diversity, or (2) disturbances, but not stability, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 contribute to species diversity. The reason for the ambiguity is the use of an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 improper correlative as well as faulty parallelism (from appears only in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 first correlative term). The correct answer choice must make the sentence’s 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 meaning clear, probably by using one of two correlatives: not only . . . but 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 also or not . . . but rather. Also, the two correlative terms must be parallel. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (E) corrects the faulty parallelism (from appears in each correlative term) 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and clears up the sentence’s meaning. Although (B) corrects the parallelism 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 problem, it uses the nonsensical (and improper) correlative not only . . . 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 but instead. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Redundancy, Wordiness, Awkwardness, and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 Omissions 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In addition to covering grammar and sentence structure, GM AT Sentence 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Correction also tests you on your skill at recognizing and fixing the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following types of problems involving written expression: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Redundancy (repeating the same idea) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Wordiness (using more words than needed to make the point) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Awkwardness (using clumsy, confusing, or overly complicated 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wording) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • O missions (omitting words that are needed for clarity or sentence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The problems of wordiness and awkwardness will show up in the majority 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the 14–15 Sentence Correction questions on the GM AT. So always be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on the lookout for them in both the original sentences or in one or more of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 the answer choices. 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 397

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Redundant Words and Phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for words and phrases that express the same idea twice. This 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 syndrome is known as “ redundancy.” In many cases, correcting the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem is as simple as omitting one of the redundant phrases. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 redundant: T he reason that we stopped for the night was because we 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 were sleepy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 redundant: Because we were sleepy, we therefore stopped for the night. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 better: We stopped for the night because we were sleepy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 redundant: The underlying motive behind his seemingly generous offer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 was old-fashioned greed. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: The motive behind his seemingly generous offer was old2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 fashioned greed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: The underlying motive for his seemingly generous offer was 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 old-fashioned greed. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 redundant: O ne of the fossils is twenty thousand years old in age. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: O ne of the fossils is twenty thousand years old. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 redundant: The German O ktoberfest takes place each O ctober of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 every year. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 better: The German O ktoberfest takes place every O ctober. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 redundant: A t the sam e tim e that lightning struck, we sim ultaneously 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lost our electric power. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: At the same time that lightning struck, we lost our electric 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 power. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 redundant: Both unemployment as w ell as interest rates can affect 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stock prices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: Both unemployment levels and interest rates can affect stock 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prices. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: Unemployment levels as well as interest rates can affect stock 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prices. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 redundant: N ot only does dinner smell good, but it also tastes good 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 too. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 better: N ot only does dinner smell good, but it tastes good too. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 398 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Alert!

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow look at a GM AT-style sentence that raises the issue of redundancy. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Due to a negligible difference in Phase III results as between patients 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 using the drug and those using a placebo, the Food and Drug 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Administration refused to approve it on this basis. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Due to a negligible difference in Phase III results between 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 patients using the drug and those using a placebo, the Food 2 12345678901234567890123456789012123456789012345678901 2 and Drug Administration refused to approve the drug on this 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 basis. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. The Food and Drug Administration refused to approve the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 drug based upon a negligible difference in Phase III results as 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between patients using it and those using a placebo. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. Due to a negligible difference in Phase III results as between 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 patients using the drug and those using a placebo, the Food 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and Drug Administration refused to approve the drug. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. There are three distinct problems with the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 original version. First, due to and on this basis serve the same function—to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 express that the FDA’s refusal was based on the Phase III results. (The 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 redundancy is easy to miss since one phrase begins the sentence while the 2 12345678901234567890123456789012123456789012345678901 other phrase ends it.) Secondly, the intended antecedent of it is the drug, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but the intervening noun placebo obscures the reference. Thirdly, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence is ambiguous. Did the FDA refuse to approve the drug, or did it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 approve the drug on some basis other than the one mentioned in the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence? The sentence is ambiguous as to which meaning is intended. (C) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 corrects all three problems, simply by omitting on this basis and by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 replacing it with the drug. (B) corrects the first two problems by omitting 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 due to and reconstructing the sentence. But (B) fails to clarify the meaning 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the sentence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, be on the lookout for sentences having the following 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ themes” and keywords. Redundancies are most likely to spring up in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 these kinds of sentences: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Words establishing cause-and-effect (because, since, if, then, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 therefore) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • References to time (age, years, hours, days) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Words used in conjunctions (both, as well, too, also) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 399

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Superfluous (Unnecessary) Words 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You just took a look at one variety of unnecessary verbiage: redundancy. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow look at some other kinds of sentences in which certain words can 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 simply be omitted without affecting the meaning or effectiveness of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original sentence. Remember: Briefer is better! 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Each sentence in the first group below contains an ellipsis: a word or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrase that can be omitted because it is clearly implied. (In the incorrect 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 version, the ellipsis is italicized.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 superfluous: The warmer the weather is, the more crowded the beach is. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 concise: The warmer the weather, the more crowded the beach. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 superfluous: H e looks exactly like Francis look s. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise: H e looks exactly like Francis. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 superfluous: That shirt is the ugliest shirt that I have ever seen. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise: That shirt is the ugliest I have ever seen. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Each sentence in the next group includes a superfluous preposition. (In the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect version, the preposition is italicized.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 superfluous: The other children couldn’t help from laughing at the girl 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with mismatched shoes. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: The other children couldn’t help laughing at the girl with 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mismatched shoes. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 superfluous: O ne prominent futurist predicts a nuclear holocaust by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the year of 2020. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: O ne prominent futurist predicts a nuclear holocaust by the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 year 2020. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 superfluous: They made the discovery in around December of last year. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: They made the discovery around December of last year. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 superfluous: The waiter brought half of a loaf of bread to the table. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise: The waiter brought half a loaf of bread to the table. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 400 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Superfluous words can also appear in a series of parallel clauses. Both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 versions of the next sentence use proper parallelism, but briefer is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better—as long as the meaning of the sentence is clear. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 superfluous: M y three goals in life are to be healthy, to be wealthy, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to be wise. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 concise: M y three goals in life are to be healthy, wealthy, and wise. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere’s a GM AT-style sentence that contains superfluous words. The 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 2 2 12345678901234567890123456789012123456789012345678901 2 versions listed here. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 O nly through a comprehensive, federally funded vaccination 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 program can a new epidemic of tuberculosis be curbed, just like the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 spread of both cholera as well as the spread of typhoid was curbed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. as well as the spread of typhoid was curbed 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. and typhoid 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. as well as typhoid was curbed 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. The original sentence suffers from no fewer 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than three distinct verbiage problems. First, the correlative both . . . as w ell 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as is redundant (and improper). Since both is not underlined, as w ell as 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 should be replaced with and. Secondly, because the preposition lik e sets up 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 an ellipsis, w ere curbed is implied and can be omitted. Thirdly, the second 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 occurrence of the spread of can be omitted since it is implied through the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 use of parallel construction. (D) pares down the underlined phrase to its 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 most concise form. (E) fails to correct the redundant correlative both . . . as 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w ell as. (E) also fails to omit the unnecessary w as curbed. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Wordy and Awkward Phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Just because a sentence is grammatically acceptable, you shouldn’t assume 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that there is no room for improvement. You’ve already seen that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unnecessary words can sometimes be omitted, thereby improving a GM AT 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence. N ow, look at some phrases that can be replaced with clearer, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more concise ones. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wordy: Failure can som e of the tim e serve as a prelude to success. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 concise: Failure can som etim es serve as a prelude to success. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 401

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 wordy: A s a result of G reg’s being a compulsive overeater, it is not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lik ely that he w ill live past the age of fifty. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: Because G reg is a compulsive overeater, he is unlik ely to live 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 past the age of fifty. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 wordy: Before the mother eats, she feeds each and every one of her 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 offspring. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: Before the mother eats, she feeds each of her offspring. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wordy: There are fewer buffalo on the plains today than there ever 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 w ere before. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: There are fewer buffalo on the plains today than ever before. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 wordy: Discipline is crucial to the attainm ent of one’s objectives. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise: Discipline is crucial to attaining one’s objectives. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wordy: H er husband was waiting for her on the platform at the tim e of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the train’s arrival. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: H er husband was waiting for her on the platform w hen the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 train arrived. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awkward: Calcification is w hen (or is w here) calcium deposits form 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 around a bone. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concise: Calcification occurs w hen calcium deposits form around a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bone. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awkward: T here are eight cats in the house, of w hich only two have 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 been fed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 concise: O f the eight cats in the house, only two have been fed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 awkward: The wind poses a serious threat to the old tree, and so does 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the snow. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 awkward: The wind and snow both pose a serious threat to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 old tree. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 402 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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N ote

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, take a look at a wordy and awkward GM AT-style sentence. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To avoid confusion between oral medications, different pills’ 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 coatings should have different colors, and pills should be different 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 in shape and size. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. different pills’ coatings should have different colors, and pills 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 should be different in shape and size 2 12345678901234567890123456789012123456789012345678901 2 B. pills should differ in color as well as in shape and size 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. pills should be able to be distinguished by their color, shape, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and size 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is B. There are several problems with the original 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence. The first is that different pills’ coatings is very awkward. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Secondly, the word coatings is probably superfluous here; color suffices to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 make the point. Thirdly, have different colors is awkward (differ in color 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 would be better). Fourthly, the phrase be different is ambiguous (different 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 from what?). Finally, a parallel series including color, shape, and size 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 would be more concise and less awkward than the construction used in the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence. (B) corrects all these problems. In (D), the phrase be able to be 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 distinguished is wordy and very awkward; the phrase be distinguishable 2 12345678901234567890123456789012123456789012345678901 2 would be better. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The wordy and awkward phrases that the GM AT can throw at you are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 limited in variety only by the collective imagination of the test-makers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The phrases we’ve provided here are just a small sampling. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Omitting a Necessary Word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the flip side of redundancy and wordiness is the error of om ission. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Excluding a necessary word can obscure or confuse the meaning of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence. Check especially for the omission of key “ little” words— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prepositions, pronouns, conjunctives, and especially the word that. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 omission: The newscaster announced the voting results were incorrect. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (What did the newscaster announce: the results or the fact that the 2 2 12345678901234567890123456789012123456789012345678901 results were incorrect?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clearer: The newscaster announced that the voting results were 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 403

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Look out especially for an omission that results in an illogical comparison, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as in the following sentences. It can easily slip past you if you’re not paying 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 close attention. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 illogical: The color of the blouse is different from the skirt. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 logical: The color of the blouse is different from that of the skirt. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 illogical: China’s population is greater than any country in the world. 2 2 12345678901234567890123456789012123456789012345678901 (This sentence draws an illogical comparison between a population 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and a country and illogically suggests that China is not a country.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 logical: China’s population is greater than that of any other country in 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the world. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you’ve just seen, one little word can make all the difference! Your mind 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can easily trick you by filling in a key word that is not actually there. The 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 moral here is: Read every GM AT sentence slowly and carefully! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for GMAT Sentence Correction 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a checklist of tips for handling GM AT Sentence Correction 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions. Some of these tips reiterate suggestions made earlier— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggestions that are worth underscoring. O thers are new here. Apply these 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points of advice to Part V’s practice tests, and then review them again, just 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 before exam day. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Read the Answer Choices Very Carefully; One 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Little Word Can Make all the Difference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The difference between answer choices can be subtle: perhaps one extra 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 little word, or perhaps a word replaced by a different one. It’s easy to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 overlook these differences if you rush through a question. Take your time, 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and read carefully. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 For Each Choice, Review the Entire Sentence— 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Not Just the Underlined Part 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Sentence Correction questions are not nearly as time-consuming as 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other Verbal questions. So take your time; plug each version into the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence, then read the entire sentence. Sure, you’ll see the occasional 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choice that’s grammatically incorrect apart from the rest of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. But such cases are the exception, not the rule. 2 12345678901234567890123456789012123456789012345678901 2 1 2 404 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 10: Sentence Correction

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Choose an Answer Just Because It Fixes 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Every Flaw in the Original Version 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If the original version is flawed, it’s a sure bet that one or two of the other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices will fix the flaw but create a new flaw! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 Trust Your Ear 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If an answer choice doesn’t sound right as you read it in the context of the 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sentence, eliminate it. There’s no need to analyze it any further. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t be Thrown by a Nonsensical Answer Choice 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 If an answer choice seems confusing or unclear, don’t assume that you are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 at fault for not understanding the sentence. Some answer choices will 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 simply not make much sense. Don’t waste your time analyzing the answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice to determine why it is wrong. Eliminate it! 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Eliminate Answer Choices that Change the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Meaning of the Original Sentence 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If an answer choice alters, distorts, or confuses the meaning of the original 2 12345678901234567890123456789012123456789012345678901 sentence, it cannot be the best choice, even if it is grammatically correct. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Resolve Close Judgment Calls in Favor of Briefer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answer Choices 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If it comes down to a coin flip between two answer choices, keep your 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 penny in your pocket and select the briefer (more concisely worded) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 choice. But don’t assume that shorter choices are automatically better than 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 longer ones. Apply this technique only when your decision comes down to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that coin flip. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Never Assume the Original Sentence is Wrong 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 This is probably the most common Sentence Correction mistake among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT test-takers. There’s a tendency to assume there is a better choice 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than the original version. But keep in mind that in about one out of five 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence Correction questions, the original sentence will be better than 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 any of the four alternatives. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 405

Take It to the N ext Level

N ote

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level GM AT Sentence Correction. H ere, you’ll: 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn to recognize and fix challenging grammatical problems 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving parts of speech 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn to distinguish between verb tenses 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn to recognize and correct improper mixing and shifting of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tense, voice, and mood 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Learn to recognize and handle challenging problems involving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence structure 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll learn to: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognize and fix challenging grammatical problems involving 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 parts of speech 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Distinguish between verb tenses 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 • Recognize and correct improper mixing and shifting of tense, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 voice, and mood 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Recognize and handle challenging problems involving sentence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 structure 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1To help you focus on the specific grammatical errors or other flaws at 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1hand, we’ll simplify the Sentence Correction format by listing just three 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1answer choices, and by limiting the kinds of flaws to one or two. Actual 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1GM AT questions include five answer choices, of course. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 406

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Errors Involving Parts of Speech 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Earlier in the chapter covered grammatical errors involving parts of speech 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that are most basic and that the GM AT covers most frequently. H ere at the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ext Level, you’ll focus on the trickiest, most testworthy rules of grammar 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving pronoun choice and subject-verb agreement: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Error in choice of relative pronoun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Errors in agreement between a pronoun or com pound subject and 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 verb 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Error in Choice of Relative Pronoun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The English language includes only a handful of relative pronouns: w hich, 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 w ho, that, w hose, w hichever, w hoever, and w hom ever. Don’t worry 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about what the term “ relative pronoun” means. Instead, just remember 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the following rules about when to use each one: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1. Use w hich to refer to things. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Use either w ho or that to refer to people. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: Amanda, w hich was the third performer, was the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 best of the group. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Amanda, w ho was the third performer, was the best 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the group. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: The first employee that fails to meet his or her sales 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quota will be fired. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: The first employee w ho fails to meet his or her sales 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quota will be fired. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 3. Whether you should use w hich or that depends on what the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence is supposed to mean. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 one meaning: The third page, w hich had been earmarked, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contained several typographical errors. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 different meaning: The third page that had been earmarked 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contained several typographical errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 (The first sentence merely describes the third page as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 earmarked. The second sentence also suggests that the page 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 containing the errors was the third earmarked page.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. Whether you should use w ho (w hoever) or w hom (w hom ever) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 depends on the grammatical function of the person (or people) 2 2 12345678901234567890123456789012123456789012345678901 1 being referred to. Confused? Don’t worry; just take a look at the 2 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 407

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 sample sentences here, and you shouldn’t have any trouble 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deciding between w ho and w hom on the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: It was the chairman w hom initiated the bill. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: It was the chairman w ho initiated the bill. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 incorrect: First aid will be available to w hom ever requires it. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: First aid will be available to w hoever requires it. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: The team members from East H igh, w ho the judges 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 were highly impressed with, won the debate. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 correct: The team members from East H igh, with w hom the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 judges were highly impressed, won the debate. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O n the GM AT, to make sure that w ho (w hoever) and w hom (w hom ever) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are being used correctly, try substituting a regular pronoun, then rearrange 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the clause (if necessary) to form a simple sentence. If a subject-case 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pronoun works, then w ho (w hoever) is the right choice. O n the other 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hand, if an object-case pronoun works, then w hom (w hom ever) is the right 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice. H ere’s how it works with the foregoing sentences: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 It was the chairman w hom initiated the bill. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H e initiated the bill. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (H e is a subject-case pronoun, so w hom should be replaced with w ho.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 First aid will be available to w hom ever requires it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 She requires it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (She is a subject-case pronoun, so w hom ever should be replaced with 2 2 12345678901234567890123456789012123456789012345678901 w hoever.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The team members from East H igh, w ho the judges were highly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 impressed with, won the debate. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The judges were impressed with them . 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (Them is an object-case pronoun, so w ho should be replaced by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 w hom .) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 408 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence that focuses on a relative-pronoun 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 issue. The original version (A) is faulty, so your choice is between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 The Civil War’s bloodiest battle was initiated on behalf of those, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indentured black slaves, for who life was most precious. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. bloodiest battle was initiated on behalf of those, the indentured 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 black slaves, for who life was most precious 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. indentured black slaves, for whom life was most precious 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bloodiest battle, initiated the war’s bloodiest battle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. *** 2 12345678901234567890123456789012123456789012345678901 E. bloodiest battle was initiated on behalf of the indentured black 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 slaves, for whom life was most precious 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The original sentence suffers from two flaws. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 First, the relative pronoun w ho should be replaced with w hom . (Replace 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the last clause with: L ife w as m ost precious for them . The pronoun them is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 an object-case pronoun, so the correct choice is w hom .) Secondly, the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 word those, probably intended to refer to the slaves, should be deleted 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because it is unnecessary and because it confuses the meaning of the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sentence. The comma following those should also be omitted. (E) corrects 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 both flaws. (B) also corrects both flaws, but it radically alters the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence’s meaning, improperly suggesting that the slaves initiated the 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 bloodiest battle (rather than properly communicating that it was on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 slaves behalf that the battle was fought). 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Error in Subject-Verb Agreement (Pronoun and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Compound Subjects) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Determining whether a sentence’s subject is singular or plural isn’t always 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as simple as you might think. You can easily determine whether a personal 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pronoun such as he, they, and its is singular or plural. But other pronouns 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 are not so easily identified as either singular or plural. H ere are two lists, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 along with sample sentences, to help you keep these pronouns straight in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your mind. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Singular pronouns: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 anyone, anything, anybody 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 each 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 either, neither 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 every, everyone, everything, everybody 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 nobody, no one, nothing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what, whatever 2 12345678901234567890123456789012123456789012345678901 2 1 who, whom, whoever, whomever 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 409

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: Every possible cause has been investigated. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: Each one of the children here speak s fluent French. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: N either of the pens has any ink remaining in it. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: W hatever he’s doing is very effective. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 correct: Everything she touches turns to gold. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Even when they refer to a “ compound” subject joined by and, the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 pronouns listed above remain singular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: Each adult and child here speak s fluent French. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 correct: Every possible cause and suspect w as investigated. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Plural pronouns: 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 both 2 12345678901234567890123456789012123456789012345678901 few 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 many 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 several 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 others 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: Few would argue with that line of reasoning. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: M any claim to have encountered alien beings. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: Som e thrive on commotion, while others need quiet. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It’s especially easy to overlook a subject-verb agreement problem in a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence involving a compound subject (multiple subjects joined by 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 connectors such as the word and or the word or). If joined by and, a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compound subject is usually plural (and takes a plural verb). But if joined 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by or, either . . . or, or neither . . . nor, compound subjects are usually 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 singular. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 plural: The chorus and the introduction need improvement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 singular: Either the chorus or the introduction needs improvement. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 singular: N either the chorus nor the introduction needs improvement. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But what if one subject is singular and another is plural? Which form 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 should the verb take? H ere’s the rule: Look to see which subject is nearer 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to the verb; the verb should agree with that subject. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 plural: Either the rhythm or the lyrics need improvement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 singular: Either the lyrics or the rhythm needs improvement. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In some cases, you can’t tell whether a subject is singular or plural without 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1 looking at how it’s used in the sentence. This is true of so-called collective 2 2 410 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 nouns and nouns of quantity. These might call for either a singular verb or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a plural verb, depending on whether the noun is used in a singular or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural sense. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 correct: Four years is too long to wait. (four years used in singular 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 correct: Four years can pass by quickly. (four years used in plural 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sense) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 correct: The majority favors the Republican candidate. (m ajority used 2 2 12345678901234567890123456789012123456789012345678901 2 in singular sense) 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 correct: The majority of the voters here favor the Republican 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 candidate. (m ajority used in plural sense) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 H ere’s a GM AT-style sentence that contains a compound subject. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 versions listed here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N either his financial patron or Copernicus himself were expecting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the societal backlash resulting from him denouncing the Earth12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 centered Ptolemaic model of the universe. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. or Copernicus himself were expecting the societal backlash 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 resulting from him 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. nor Copernicus himself was expecting the societal backlash 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 resulting from his 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. nor Copernicus were expecting the societal backlash resulting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from him 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The original sentence actually contains three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 grammatical errors! First, neither should be paired with nor instead of or. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Secondly, the singular verb w as should be used instead of the plural w ere 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because neither . . . nor calls for a singular subject and because both parts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of the subject (patron and Copernicus) are singular. Thirdly, the phrase 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 him denouncing (which grammarians call a “ noun clause” ) is improper; 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 denouncing is a gerund (a verb turned into a noun by adding -ing), and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 gerunds always take possessive pronouns (his, in this case). (C) corrects all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 three errors without creating any new ones. (D) corrects the first error, but 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not the other two. Also, notice that (D) deletes him self from the original 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sentence. In doing so, (D) obscures the intended meaning of the sentence, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 which makes it clear, through the use of him self, that the word “ his” 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (appearing twice in the sentence) refers to Copernicus rather than to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 someone else. So (D) creates a new error! 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 411

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Problems Involving Tense, Voice, and Mood 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ve arrived at what some grammarians would consider the inner 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sanction of Standard Written English: tense, voice, and mood. These three 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concepts are among the trickiest covered GM AT Sentence Correction. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this section, you’ll focus on the following types of problems involving 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 these three concepts (notice the similarities): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Error in verb tense and shifting or mixing of tenses in a confusing 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 manner 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Awkward use of either the active or passive voice; needlessly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mixing the two voices 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Improper use of the subjunctive mood; needless mixing of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subjunctive mood and one of the tenses 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Error in Verb Tense and Improper Tense Shifting 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and Mixing 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Tense refers to how a verb’s form indicates the tim e fram e (past, present, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or future) of the sentence’s action. You won’t need to know the names of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the tenses for the GM AT, of course. But here they are anyway (all six of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them), in case you’re interested. N otice that we’ve used the singular form 2 2 12345678901234567890123456789012123456789012345678901 of the confusing verb to have in order to illustrate how verb form differs 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among different tenses. All of these sentences are correct. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 simple present: H e has enough money to buy a new car. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simple past: H e had enough money after he was paid to by a new car. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simple future: H e w ill have enough money after he is paid to buy a new 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 car. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 present perfect: H e has had enough food but has continued to eat 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 anyway. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 past perfect: H e had had enough food but had kept eating anyway. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 future perfect: H e w ill have had enough food once he has finished 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eating the dessert. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 412 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

N ote

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 With many verbs, the same form is used for all tenses, except that -ed is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 added for the past tenses—as in w alk , w alk ed. H owever, other verbs use 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 distinctive forms for different tenses—as in see, saw , seen. Use your ear to 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 determine whether the form sounds correct. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: The pilot seen the mountain but was flying too low to avoid 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 a collision. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: The pilot saw the mountain but was flying too low to avoid a 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 collision. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An incorrect sentence might needlessly m ix tenses or shift tense from one 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 time frame to another in a confusing manner. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: If it rains tomorrow, we cancel our plans. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: If it rains tomorrow, we w ill cancel our plans. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: When Bill arrived, Sal still did not begin to unload the truck. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: When Bill arrived, Sal still had not begun to unload the truck. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 O ur warning about mixing and shifting tenses also applies to the sentences 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 like these: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: To go to war is to have traveled to hell. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: To go to war is to go to hell. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: To have gone to war is to have traveled to hell. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: Seeing the obstacle w ould have allow ed him to alter his 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 course. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: H aving seen the obstacle w ould have allow ed him to alter his 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 course. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: Seeing the obstacle w ould allow him to alter his course. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 By the way, verbs preceded by to (for example, to go) are called 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 infinitives, and verbs turned into nouns by tacking an -ing the end (for 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 example, seeing) are called gerunds. O f course, you don’t need to know 2 12345678901234567890123456789012123456789012345678901 that for the GM AT. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 413

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow look at how a tense-shift problem might appear in a GM AT-style 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. The original version (A) is faulty, so your choice is between the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Companies that fail in their making cost-of-living adjustments of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 salaries of workers could not attract or retain competent employees. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. fail in their making cost-of-living adjustments of salaries of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 workers could not 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. *** 2 12345678901234567890123456789012123456789012345678901 2 C. *** 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. will fail to adjust worker salaries to reflect cost-of-living 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 changes can neither 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. fail to make cost-of-living adjustments in their workers’ 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 salaries cannot 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The original sentence mixes present tense (fail) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with past tense (could not attract). Also, the phrases fail in their m ak ing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and of salaries of w ork ers are awkward and unnecessarily wordy. (E) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 renders the sentence consistent in tense by replacing could with can. (E) is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 also more concise than the original sentence. (D) improperly mixes future 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tense (w ill fail) with present tense can . . . retain. (D) also uses neither to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 form the improper correlative pair neither . . . or. (The proper correlative 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pair is neither . . . nor.) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Inappropriate Use of the Passive Voice 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In a sentence expressed in the active voice, the subject “ acts upon” an 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 object. Conversely, in a sentence expressed in the passive voice, the subject 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ is acted upon” by an object. The passive voice can sound a bit awkward, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 so the active voice is generally preferred. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 passive (awkward): The book was read by the student. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 active (better): The student read the book. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passive (awkward): Repetitive tasks are performed tirelessly by 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 computers. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 active (better): Computers perform repetitive tasks tirelessly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ixing the active and passive voices results in an even more awkward 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 mixed (awkward): Although the house was built by Gary, Kevin built 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the garage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 414 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 passive (less awkward): Although the house was built by Gary, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 garage was built by Kevin. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 active (best): Although Gary built the house, Kevin built the garage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the active voice is usually less awkward than the passive voice, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sometimes the passive voice is appropriate for emphasis or impact. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 active (less effective): Yesterday a car hit me. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passive (more effective): Yesterday I was hit by a car. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passive (more effective): Sunrise over the Tetons is surpassed in beauty 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 only by the sun itself. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 active (less effective): O nly the sun itself surpasses the Tetons in beauty. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep in mind that the passive voice is not grammatically wrong. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So don’t eliminate an answer choice merely because it uses the passive 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 voice. Check for grammatical errors among all five choices. If the one that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uses the passive voice is the only one without a grammatical error, then 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 it’s the best choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a GM AT-style sentence that focuses on the use of the passive voice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 It is actually a chemical in the brain that creates the sensation of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eating enough, a chemical that is depleted by consuming simple 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 sugars. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. It is actually a chemical in the brain that creates the sensation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of eating enough, a chemical that is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. The sensation of having eaten enough is actually created by a 2 12345678901234567890123456789012123456789012345678901 2 chemical in the brain that is 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. A chemical actually creates the sensation in the brain of having 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 eaten enough, and this chemical is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. The original sentence isn’t terrible, but it 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 includes two flaws. First, the awkward eating enough should be replaced; 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 having eaten enough is the proper idiom here. Both (C) and (D) correct this 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 flaw. Second, notice that a chem ical appears twice in the sentence. A more 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 effective sentence would avoid repetition. O nly (C) avoids repeating this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 phrase by reconstructing the first clause. In doing so, (C) admittedly uses 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 the passive voice. N evertheless, (C) is more concise and less awkward 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 415

Take It to the Next Level

Alert!

Chapter 10: Sentence Correction

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 overall than the original sentence. O ne more point about (D): It also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 creates a new problem. It separates the sensation from of having eaten 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enough, thereby creating an awkward and confusing clause. The phrase in 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 the brain should be moved to either an earlier or later position in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Error in Using the Subjunctive Mood 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The subjunctive m ood should be used to express a w ish or a contrary-to- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fact condition. These sentences should include words such as if, had, w ere 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and should. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: I wish it w as earlier. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: I wish it w ere earlier. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: Suppose he speeds up suddenly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: Suppose he w ere to speed up suddenly. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: If the college lowers its tuition, I would probably enroll. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 correct: Should the college lower its tuition, I w ould probably enroll. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: If the college w ere to lower its tuition, I w ould probably 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enroll. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 incorrect: H ad he driven slower, he will recognize the landmarks from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now on. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: H ad he driven slower, he w ould recognize the landmarks from 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now on. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: If he had driven slower, he w ould recognize the landmarks 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from now on. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 416 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The subjunctive mood can be tricky because it uses its own idiomatic verb 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 forms and because you can’t always trust your ear when it comes to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 catching an error. Just remember: If the sentence uses a regular verb tense 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (past, present, future, etc.) to express a wish or contrary-to-fact 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 condition, then it is grammatically incorrect, even if the subjunctive verb 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 form is also used. Look, for example, at the incorrect sample sentences 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from above. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • I wish it w as earlier. (It w as earlier uses past tense.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Suppose he speeds up suddenly. (H e speeds up quick ly uses present 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 tense.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • If the college lowers its tuition, I would probably enroll. (The first 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clause uses present tense, while the second clause uses subjunctive 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 form.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • H ad he driven slower, he will recognize the landmarks from now 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on. (The first clause uses subjunctive form, while the second clause 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uses future tense.) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The subjunctive mood is also used in clauses of recommendation, request, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggestion, or demand. These clauses should include the word that: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: Ann suggested we should go to the Chinese restaurant. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: Ann suggested that we go to the Chinese restaurant. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 incorrect: I insist you be quiet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 correct: I insist that you be quiet. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrect: The supervisor preferred all workers wear uniforms from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now on. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: The supervisor preferred that all workers wear uniforms from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 now on. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 417

Take It to the Next Level

Tip

Chapter 10: Sentence Correction

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence designed to test you on the use of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subjunctive mood. The original version (A) is faulty, so your choice is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between the two alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Environmental Protection Agency would be overburdened by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 its detection and enforcement duties if it fully implemented all of its 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 own regulations completely. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. if it fully implemented all of its own regulations completely 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 B. if it was to implement all of its own regulations completely 2 12345678901234567890123456789012123456789012345678901 2 C. were it to fully implement all of its own regulations 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The original sentence poses two problems. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 First, the sentence clearly intends to express a hypothetical or contrary-to- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fact situation; yet the underlined phrase does not use the subjunctive w ere. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Secondly, fully and com pletely are redundant; one of them should be 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deleted. (C) corrects both problems without creating a new one. (B) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corrects the redundancy problem by deleting fully. H owever, it incorrectly 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uses w as instead of the subjunctive w ere. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Sentence Structure and Sense 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Sentence structure refers to how a sentence’s parts fit together as a whole. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 You know a sentence is poorly structured when its ideas are confusing, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 vague, ambiguous, or nonsensical—or even when its structure places 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 undue emphasis (or de-emphasis) on certain ideas. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Problems involving sentence structure can be challenging to fix because 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 there are no hard-and-fast rules of grammar to tell you what the best 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution is. And since there are many acceptable ways to make any 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement, the distinction between a highly effective structure and a less 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 effective one can be subtle. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere are the specific types of structural problems you’ll examine in this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 section: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Improper placement of modifiers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Confusing pronoun references 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Dangling modifier errors 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Rhetorical imbalance between sentence parts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Improper splitting of a grammatical unit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Too many subordinate clauses in a row 2 1 2 418 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Improper Placement of Modifiers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A m odifier is a word or phrase that describes, restricts, or qualifies another 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 word or phrase. M odifying phrases are typically set off with commas, and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 many such phrases begin with a relative pronoun (w hich, w ho, that, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 w hose, and w hom ). M odifiers should generally be placed as close as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possible to the word(s) they modify. Positioning a modifier in the wrong 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 place can result in a confusing or even nonsensical sentence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 misplaced: H is death shocked the entire family, which occurred quite 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 suddenly. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: H is death, which occurred quite suddenly, shocked the entire 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 family. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 misplaced: N early dead, the police finally found the victim. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 better: The police finally found the victim , w ho w as nearly dead. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unclear: Bill punched Carl while wearing a mouth protector. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clear: While wearing a mouth protector, Bill punched Carl. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M odifiers such as alm ost, nearly, hardly, just and only should immediately 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 precede the word(s) they modify, even if the sentence sounds correct with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the parts separated. For example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 misplaced: Their one-year old child alm ost weighs forty pounds. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 better: Their one-year old child weighs alm ost forty pounds. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ote the position of only in the following sentences: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear: O nly the assistant was able to detect obvious errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 unclear: The assistant was only able to detect obvious errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 unclear: The assistant was able to only detect obvious errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clear: The assistant was able to detect only obvious errors. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 419

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence that misplaces a modifier. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Exercising contributes frequently to not only a sense of well being 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but also to longevity. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. Exercising contributes frequently to not only a sense of well 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 being but also to longevity. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. *** 2 12345678901234567890123456789012123456789012345678901 C. Exercising frequently contributes not only to a sense of well 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 being but to longevity. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 D. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Frequent exercise contributes not only to a sense of well being 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but also to longevity. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. In the original sentence, frequently is probably 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 intended to describe (or modify) ex ercising (frequent exercise). But 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 separating these words makes it appear as though frequently describes 2 2 12345678901234567890123456789012123456789012345678901 contributing, which makes no sense in the overall context of the sentence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The original sentence also contains a “ parallelism” error. The phrase after 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not only should parallel the phrase after but also, so that the two phrases 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can be interchanged and still make sense grammatically. But in the original 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence, the two phrases are not parallel. (E) corrects both problems. In 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (E), it is clear that what is “ frequent” is ex ercise (rather than contributing). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, the phrases following each part of the not only . . . but also pair are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 now parallel. (N otice that each phrase begins with to.) (C) fails to clear up 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the confusion as to whether frequently describes ex ercising or contributes. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Also, (C) improperly uses not only . . . but instead of the proper idiom not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 only . . . but also. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The general rule about placing modifiers near the words they modify 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 applies m ost of the time. In some cases, however, trying to place a 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 modifier near the words it modifies actually confuses the meaning of the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence, as with the modifier w ithout his glasses in the sentences below. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unclear: N athan can read the newspaper and shave w ithout his 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 glasses. (It is unclear whether w ithout his glasses refers only to shave 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 or to both shave and read the new spaper.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 unclear: W ithout his glasses, N athan can read the newspaper and can 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shave. (This sentence implies that these are the only two tasks N athan 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 can perform without his glasses.) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clear: Even w ithout his glasses, N athan can read the newspaper and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 shave. It is important not to apply the modifier rule mechanically. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Instead, check to see whether the sentence as a whole makes sense. 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 420 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Confusing Pronoun Reference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A pronoun (e.g., she, him , their, its) is a “ shorthand” way of referring to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an identifiable noun—-person(s), place(s) or thing(s). N ouns to which 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 pronouns refer are called antecedents. M ake sure every pronoun in a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence has a clear antecedent! 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 unclear: M inutes before Kevin’s meeting with Paul, his wife called with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the bad news. (Whose wife called—Kevin’s or Paul’s?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 clear: Kevin’s wife called with the bad news minutes before his meeting 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with Paul. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 clear: M inutes before Kevin’s meeting with Paul, Kevin’s wife called 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with the bad news. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Pronoun reference errors are usually corrected in one of two ways: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. By placing the noun and pronoun as near as possible to each 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other without other nouns coming between them (second 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence above) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2. By replacing the pronoun with its antecedent (third sentence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 above) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Also, look for the vague use of it, you, that or one—-without clear 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reference to a particular antecedent. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 vague: When one dives in without looking ahead, you never know 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what will happen. (Does you refer to the diver or to the broader one?) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clear: O ne never knows what will happen when one dives in without 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 looking ahead. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clear: When you dive in without looking ahead, you never know what 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 will happen. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 vague: When the planets are out of alignment, it can be disastrous. (It 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 does not refer to any noun.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 clear: Disaster can occur when the planets are out of alignment. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 421

Part IV: Verbal A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The following GM AT-style sentence contains more than one confusing 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pronoun reference. The original version (A) is faulty, so your choice is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between the two alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E-mail accounts administered by an employer belong to them, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they can be seized and used as evidence against the employee. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. an employer belongs to them, and they can be seized and used 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. employers belong to them, who can seize and use it 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. an employer belong to the employer, who can seize and use the 2 12345678901234567890123456789012123456789012345678901 2 accounts 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. There are two pronoun problems in the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original sentence. First, them is used vaguely, without clear reference to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 em ployers, which seems to be the intended antecedent. Adding to this 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 confusion is that the pronoun them is plural, yet its intended antecedent 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 em ployer is singular. In addition, the antecedent of they is unclear because 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it is separated from its intended antecedent, accounts, by two other nouns 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (them and em ployer). (C) corrects the first problem by replacing the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pronoun them with its (singular) antecedent em ployer. (C) also corrects 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the second problem by using w ho, which clearly refers to em ployer, since 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the two words appear immediately next to each other. (B) is riddled with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems! First, (B) does not correct the vague use of them (although the 2 2 12345678901234567890123456789012123456789012345678901 use of the plural em ployers is an improvement). Second, (B) leaves it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unclear as to which noun w ho refers; presumably, w ho refers to them , yet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the antecedent of them is uncertain. Thirdly, although the pronoun it is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 intended to refer to accounts, the reference is unclear because the pronoun 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and antecedent are separated by other nouns. Finally, the pronoun it is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 singular, yet its antecedent accounts is plural (they should both be either 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 singular or plural). 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 When you see a pronoun in a GM AT sentence, ask yourself: “ To what 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 noun does this pronoun refer?” If the answer is the least bit unclear, you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can rule out that version of the sentence as the best choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 422 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Dangling Modifier Errors 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A dangling m odifier is a modifier that doesn’t refer to any particular 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 word(s) in the sentence. The best way to correct a dangling-modifier 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem is to reconstruct the sentence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dangling: Set by an arsonist, firefighters were unable to save the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 burning building. (This sentence makes no reference to whatever was 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 set by an arsonist.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 better: Firefighters were unable to save the burning building from the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fire set by an arsonist. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Despite the rule against dangling modifiers, certain dangling modifiers are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 acceptable because they’re idiomatic. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 acceptable: Judging from the number of violent crimes committed 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 every year, our nation is doomed. (Although the sentence makes no 2 2 12345678901234567890123456789012123456789012345678901 reference to whomever is judging, it is acceptable anyway.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 acceptable: Considering that star’s great distance from the earth, its 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 brightness is amazing. (Although this sentence makes no reference to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 whomever is considering, it is acceptable anyway.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you encounter a dangling modifier in a GM AT sentence that you’ve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 heard many times from well-educated people, then it’s probably one of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 those idiomatic exceptions to the prohibition against dangling modifiers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence that contains a dangling modifier. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 By imposing artificial restrictions in price on oil suppliers, these 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suppliers will be forced to lower production costs. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. By imposing artificial restrictions in price on oil suppliers, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these suppliers will be forced 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Imposing artificial price restrictions on oil suppliers will force 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 these suppliers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. By imposing on oil suppliers artificial price restrictions, these 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 suppliers will be forced 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. *** 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 423

Take It to the Next Level

Tip

Chapter 10: Sentence Correction

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. The original sentence includes a dangling 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 modifier. The sentence makes no reference to whomever (or whatever) is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 imposing the price restrictions. (B) corrects the problem by reconstructing 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 the sentence. (B) also improves on the original sentence by replacing 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 restrictions in price with the more concise price restrictions. (C) does not 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct the dangling modifier problem. Also, the grammatical construction 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 of the first clause in (C) is awkward and confusing. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Rhetorical Imbalance Between Sentence Parts 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 An effective sentence gets its point across by placing appropriate emphasis 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 on its different parts. If you’re dealing with two equally important ideas, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 they should be separated as two distinct “ main clauses,” and they should 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 be similar in length (to suggest equal importance). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 unbalanced: Julie and Sandy were the first two volunteers for the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 fund-raising drive, and they are twins. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 balanced: Julie and Sandy, w ho are twins, were the first two volunteers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 for the fund-raising drive. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 commingled (confusing): Julie and Sandy, w ho are twins, are 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 volunteers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 separated (balanced): Julie and Sandy are twins, and they are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 volunteers. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 O n the other hand, if you’re dealing with only one main idea, be sure 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that it receives greater emphasis (as a main clause) than the other ideas 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the sentence. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 equal emphasis (confusing): Jose and Victor were identical twins, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they had completely different ambitions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 emphasis on second clause (better): A lthough Jose and Victor were 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 identical twins, they had completely different ambitions. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 424 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 10: Sentence Correction

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a GM AT-style example of a rhetorically-challenged sentence. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two alternative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 versions listed here. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Treating bodily disorders by non-invasive methods is generally 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 painless, and these methods are less likely than those of conven2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 tional Western medicine to result in permanent healing. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Treating bodily disorders by non-invasive methods is generally 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 painless, and these methods 2 12345678901234567890123456789012123456789012345678901 2 B. Treating bodily disorders by non-invasive methods is generally 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 painless, but they 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 C. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. *** 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Although treating bodily disorders by non-invasive methods is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 generally painless, these methods 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. N otice that the original sentence contains two 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 main clauses, connected by and. Two problems should have occurred to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you as you read the sentence: (1) the connector and is inappropriate to 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 contrast differing methods of treatment (it fails to get the point across), 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and (2) the second clause expresses the more important point but does not 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 receive greater emphasis than the first clause. (E) corrects both problems 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 by transforming the first clause into a subordinate one and by eliminating 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the connecting word and. What about choice (B)? Replacing and with but 2 12345678901234567890123456789012123456789012345678901 is not as effective in shifting the emphasis to the second clause as the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 method used in (B). M oreover, by replacing these m ethods with they, (B) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 creates a pronoun-reference problem, making it unclear whether they 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refers to disorders or to m ethods. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Improper Splitting of a Grammatical Unit 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Splitting clauses or phrases (by inserting another clause between them) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 often results in an awkward and confusing sentence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 split: The value of the dollar is not, relative to other currencies, rising 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 universally. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 better: The value of the dollar is not rising universally relative to other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 currencies. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 split: The government’s goal this year is to provide for its poorest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 residents an econom ic safety net. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 split: T he governm ent’s goal is to provide an economic safety net this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 year for its poorest residents. 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 425

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 better: The government’s goal this year is to provide an economic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 safety net for its poorest residents. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In GM AT sentences, look closely for split infinitives. An infinitive is the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 plural form of an action verb, preceded by the word “ to.” If to is separated 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from its corresponding verb, then you’re dealing with a “ split infinitive” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 and the sentence is grammatically incorrect! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 improper (split): The executive was compelled to, by greed and 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 ambition, w ork more and more hours each day. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: The executive was compelled by greed and ambition, to w ork 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more and more hours each day. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 improper (split): M eteorologists have been known to inaccurately 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 predict snowstorms. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct: M eteorologists have been known to predict snowstorms 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inaccurately. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence with a split personality. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 original version (A) is faulty, so your choice is between the two 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Typographer Lucian Bernhard was influenced, perhaps more so 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than any of his contemporaries, by Toulouse-Lautrec’s emphasis on 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 large, unharmonious lettering. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Typographer Lucian Bernhard was influenced, perhaps more so 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 than any of his contemporaries, by Toulouse-Lautrec’s 2 12345678901234567890123456789012123456789012345678901 emphasis on large, unharmonious lettering. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Perhaps more so than any of his contemporaries, typographer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Lucian Bernhard was influenced by Toulouse-Lautrec’s 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 emphasis on large, unharmonious lettering. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. *** 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Typographer Lucian Bernhard was influenced by Toulouse12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Lautrec’s emphasis on large, unharmonious lettering perhaps 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more so than any of his contemporaries. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. The original sentence awkwardly splits the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 main clause with an intervening subordinate one (set off by commas). Both 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (B) and (E) keep the main clause intact. H owever, (E) creates a pronoun 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reference problem: It’s unclear as to whom the pronoun his refers— 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Bernhard or Toulouse-Lautrec. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 426 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Whenever you see a clause set off by commas in the middle of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence, check the words immediately before and after the clause. If 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 keeping those words together would sound better to your ear or would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more effectively convey the sentence’s main point, then the sentence 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (answer choice) is wrong, and you can safely eliminate it! 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Too Many Subordinate Clauses in a Row 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 A subordinate clause is one that does not stand on its own as a complete 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentence. Stringing together two or more subordinate clauses can result in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 an awkward and confusing sentence. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 awkward: Barbara’s academic major is history, w hich is a very popular 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 course of study among liberal arts students, w ho are also contributing to 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the popularity of political science as a major. 2 12345678901234567890123456789012123456789012345678901 better: Barbara’s academic major is history, which along with political 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science, is a very popular course of study among liberal arts students. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ow, look at a GM AT-style sentence that suffers from this sort of error. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 The original version (A) is faulty, so your choice is between the two 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alternative versions listed here. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 By relying unduly on anecdotal evidence, which often conflicts with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more reliable data, including data from direct observation and 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 measurement, a scientist risks losing credibility among his or her 2 12345678901234567890123456789012123456789012345678901 2 peers. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. By relying unduly on anecdotal evidence, which often conflicts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with more reliable data, including data from direct observation 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and measurement, a scientist risks losing credibility among his 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 or her peers. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. *** 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. *** 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. A scientist, by relying unduly on anecdotal evidence, which 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 often conflicts with more reliable data, including data from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 direct observation and measurement, risks losing credibility 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 among his or her peers. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. A scientist risks losing credibility among his or her peers by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relying unduly on anecdotal evidence, which often conflicts 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with more reliable data, including data from direct observation 2 2 12345678901234567890123456789012123456789012345678901 and measurement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 427

Take It to the Next Level

Tip

Chapter 10: Sentence Correction

Part IV: Verbal A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. The original sentence contains four clauses 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (separated by commas). The first three are all subordinate clauses! The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 result is that you are left in suspense as to who unduly relies on anecdotal 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 evidence (first clause) until you reach the last (and main) clause. The 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution is to rearrange the sentence to join the first and last clause, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thereby minimizing the string of subordinate clauses and eliminating 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 confusion. Choice (E) provides this solution. Choice (D) solves the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem only partially by moving only a section of the main clause (the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 scientist) to the beginning of the sentence. In fact, by doing so, (D) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 probably creates more confusion. Do you agree? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Subordination of a dependent clause to a main clause can be achieved 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 through the use of: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Words modifying relative pronouns: w hich, w ho, that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Words establishing time relationship: before, after, as, since 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Words establishing a causal relationship: because, since 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Words of admission or concession: although, though, despite 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Words indicating place: w here, w herever 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Words of condition: if, unless 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 428 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter

11 Reading Comprehension

X-Ref

123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to GM AT Reading Comprehension. H ere, you’ll learn: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The importance of reading GM AT passages “ interactively” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A step-by-step approach to handling Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Techniques for reading more effectively and efficiently 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Success keys for GM AT Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The interactive reading techniques you’ll learn here will help you handle 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 any of the question types the test might deal you. O nce you’ve mastered 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 these techniques, move ahead to the N ext Level to take a closer look at 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the test-maker’s favorite question types and wrong-answer ploys. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “Inter active” Reading: The Key to Reading 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 Comprehension 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you’re like most GM AT test-takers, you’ll experience at least one of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following problems as you tackle Reading Comprehension: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your concentration is poor—perhaps due to your lack of familiar2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ity with or interest in the topic, or perhaps due to general test 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 anxiety. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Your reading pace is slow—so you have trouble finishing the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Verbal section in time. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • To answer each question, you find yourself searching the passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 again and again to find the information you need. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • You have trouble narrowing down the answer choices to one that’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 clearly the best. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 429

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Believe it or not, all of these problems are due to the same bad habit: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passive reading, by which you simply read the passage from start to finish, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 giving equal time and attention to every sentence without thought as to 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 what particular information might be key in answering the questions. You 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 might call this approach the “ osmosis strategy,” since you’re hoping to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 absorb what you need to know by simply allowing your eyes to glaze over 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the words. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s the likely result of this osmosis strategy? You might remember 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 some scattered facts and ideas, which will help you respond correctly to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some easier questions. But the passive mind set won’t take you very far 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 when it comes to most of the questions, which measure your ability to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 understand the ideas in the passage rather than to simply recall 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information. Understanding a passage well enough to answer all the 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions requires a highly active frame of mind—one in which you 2 2 12345678901234567890123456789012123456789012345678901 constantly interact with the text as you read, asking yourself questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 such as these: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What’s the passage’s main idea (or “ thesis” ) and the author’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 overall concern or purpose? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What does each part of the passage relate to the main idea and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author’s overall purpose? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • What’s the author’s line of reasoning, or so-called “ train of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thought” ? 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Interactive reading is the key to handling GM AT Reading Comprehension, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and that’s what this chapter is primarily about! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t except to just walk into the GM AT testing room and apply the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 techniques you’ll learn about here without practicing them first. You’ll 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 need to try them out first, during your GM AT practice testing, until you 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 become comfortable with them. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 430 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Reading Comprehension—Your 7-Step 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Game Plan 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The first task in this chapter is to learn the seven basic steps for handling a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT Reading Comprehension passage and question set. You’ll apply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these steps to the following sample passage and three questions: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Passage lines are always numbered as shown here because questions 2 12345678901234567890123456789012123456789012345678901 occasionally refer to portions of the passage by line number. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Passage 1 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Line The encounter that a portrait records is most tangibly the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sitting itself, which may be brief or extended, collegial or 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 confrontational. Renowned photographer Cartier-Bresson has 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 expressed his passion for portrait photography by characteriz12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 ing it as “ a duel without rules, a delicate rape.” Such meta(5) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 phors contrast quite sharply with Richard Avedon’s conception 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of a sitting. While Cartier-Bresson reveals himself as an 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 interloper and opportunist, Avedon confesses—perhaps 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uncomfortably—to a role as diagnostician and (by implication) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 psychic healer: not as someone who necessarily transforms his (10) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subjects, but as someone who reveals their essential nature. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Both photographers, however, agree that the fundamental 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 dynamic in this process lies squarely in the hands of the artist. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A quite-different paradigm has its roots not in confronta2 12345678901234567890123456789012123456789012345678901 tion or consultation but in active collaboration between the (15) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 artist and sitter. This very different kind of relationship was 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 formulated most vividly by William H azlitt in his essay entitled 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ O n Sitting for O ne’s Picture” (1823). To H azlitt, the “ bond 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of connection” between painter and sitter is most like the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relationship between two lovers. H azlitt fleshes out his thesis (20) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 by recalling the career of Sir Joshua Reynolds. According to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H azlitt, Reynold’s sitters were meant to enjoy an atmosphere 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 that was both comfortable for them and conducive to the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 enterprise of the portrait painter, who was simultaneously their 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 host and their contractual employee. (25) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 431

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 1. The author of the passage quotes Cartier-Bresson (line 5) in order to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. refute Avedon’s conception of a portrait sitting. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. provide one perspective of the portraiture encounter. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. support the claim that portrait sittings are, more often than 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not, confrontational encounters. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 D. show that a portraiture encounter can be either brief or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 extended. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. distinguish a sitting for a photographic portrait from a sitting 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 for a painted portrait 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. Which of the following characterizations of the portraiture experi2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 ence as viewed by Avedon is most readily inferable from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage? 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. A collaboration 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. A mutual accommodation 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. A confrontation 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. An uncomfortable encounter 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 E. A consultation 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3. Which of the following best expresses the passage’s main idea? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. The success of a portrait depends largely on the relationship 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between artist and subject. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. Portraits, more than most other art forms, provide insight into 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the artist’s social relationships. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 C. The social aspect of portraiture sitting plays an important part 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the sitting’s outcome. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. Photographers and painters differ in their views regarding their 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 role in portrait photography. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The paintings of Reynolds provide a record of his success in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 achieving a social bond with his subjects. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: Read the first question (including the answer choices), before you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 begin reading the passage. Try to anticipate what the passage is about and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 what sort of information you should be on the lookout for in order to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the first question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 2: Begin reading the passage, actively thinking about a possible 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thesis (main idea) and how the author attempts to support that thesis. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, begin your reading with an eye for information useful in answering 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the first question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: When you think you’ve learned enough to take a stab at the first 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question, go ahead and choose a tentative answer. You probably won’t 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 432 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 have to read very far to at least take a reasoned guess at the first question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 But don’t confirm your selection yet! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 4: Read the remainder of the passage, formulating an outline as you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 go. As you read, try to (1) separate main ideas from supporting ideas and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examples; (2) determine the basic structure of the passage (e.g., chronol12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 ogy of events, classification of ideas or things, comparison between two or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more ideas, events, or things); and (3) determine the author’s opinion or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position on the subject. M ake notes on your scratch paper as needed to see 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the flow of the passage and to keep the passage’s details straight in your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mind. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 Step 5: Sum up the passage; formulate a brief thesis (main idea) 2 2 12345678901234567890123456789012123456789012345678901 statement. Take a few seconds to review your outline. Then, in your own 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 words, express the author’s main point—in one sentence. Jot it down on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your scratch paper. Your thesis statement should reflect the author’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opinion or position (e.g., critical, supportive, neutral) toward the ideas 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 presented in the passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 6: Confirm your selection for the first question. Eliminate any 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choice that is inconsistent with your thesis statement, that doesn’t 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 respond to the question, or that doesn’t make sense to you. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 7: M ove on to the remaining question(s), considering all of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choices for each question. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you advance to the N ext Level, you’ll learn some tips to help you tackle 2 12345678901234567890123456789012123456789012345678901 different question types and to zero in on the best answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N ow let’s walk through Passage 1 (involving portraiture) and the sample 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 questions about it, using this 7-step approach. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Step 1: The first question tells you a lot about what you might expect in 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the passage. In all likelihood, the passage will be primarily about the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 portraiture experience. The author will probably provide different 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 viewpoints and insights on this experience from the perspective of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 particular artists. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Step 2: The first four sentences (lines 1–11) reinforce your initial 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prediction about the passage’s content. Based on these initial lines, it 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 appears that the author will indeed be comparing and contrasting different 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 views of the portraiture experience. At this point you don’t know whether 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the passage will involve the views of any artists other than Cartier-Bresson 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 433

Part IV: Verbal A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and Richard Avedon, nor do you know whether the author has any 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 opinion on the subject. But you should be on the lookout for answers to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 these unknowns during Step 4. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Step 3: Consider question 1 based on what you’ve read so far. The author 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 points out in lines 4–9 that Cartier-Bresson’s conception is quite different 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 from that of Avedon. Choices (A), (B), and (C) all appear to be viable 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices, at least based on lines 4–9. But whether the author’s purpose here 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is to refute Avedon’s view (choice (A)), support Cartier-Bresson’s view 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (choice (C)), or simply provide one of at least two perspectives without 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 taking sides (choice (B)) remains to be seen. You’ll have to read on to find 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 out. In any event, you can probably eliminate (D) and (E), since neither 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 one seems relevant to the Cartier-Bresson quotation. Don’t confirm a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 selection yet; go on to Step 4. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 4: Your goal in Step 4 is to formulate an informal outline of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage as you read from start to finish. You might want to jot down some 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 key words and phrases to help you see how the ideas flow and to keep the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 four individuals discussed in the passage straight in your mind. H ere’s a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 good outline of the passage: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Paragraph 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Contrast: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 — CB: confrontation (rape) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 — Avedon: diagnosis (consultation) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 — BUT agree artist is key 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Paragraph 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 3rd view: Hazlitt (writer) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 — collaboration (like lovers) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 — e.g. Reynolds 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ake outlines and summaries as brief as possible. Don’t write complete 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentences; rather, just jot down key words. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 5: N ow let’s sum up the passage based on the outline you formulated 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in Step 4. It’s a good idea to jot it down. N otice that the “ thesis” is neutral; 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the author does not side with any viewpoint presented in the passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 434 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Thesis: Portraiture is a social experience, but artists 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 disagree about their role in it. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 6: H aving read the entire passage, return to the question. N owhere 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the passage does the author attempt to either refute or support any of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the viewpoints presented. So you can eliminate (A) and (C). Accordingly, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (B) provides the best answer to the question. N otice also that (B) is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 consistent with our thesis statement. Regardless of the particular question, 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 you can eliminate any answer choice that is inconsistent with your thesis 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 7: M ove ahead to questions 2 and 3. In the following analysis, notice 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the qualitative difference (from best to worst) among the answer choices. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Also, note how we’ve labeled (in italics) what’s wrong with some of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 wrong-answer choices; you’ll learn more about these and other wrong12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 answer ploys if you advance to the N ext Level. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 2: The correct answer is E. In the first sentence of the second 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 paragraph, the author distinguishes a “ quite-different paradigm” (that is, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the case of Reynolds) from the conceptions of Cartier-Bresson and Avedon 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 in that the Reynolds paradigm “ has its roots not in confrontation or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 consultation but in active collaboration between artist and sitter.” The 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 third sentence of the passage makes clear that Cartier-Bresson conceives 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the encounter as “ confrontational” ; thus, you can reasonably infer that the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author characterizes an Avedon sitting as a “ consultation.” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (B) is also a good response but nevertheless not as good as (E). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the term “ mutual accommodation,” which does not appear in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the passage, is not altogether inconsistent with Avedon’s view, the term 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suggests a relationship in which both artist and painter allow for the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other’s needs or desires. Such a description is closer to H azlitt’s analogy of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 two lovers than to Avedon’s view of the artist as diagnostician and psychic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 healer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (A) also has merit, yet it is not as good a response as either (B) or 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (E). Admittedly, the idea of “ a collaboration” is not in strong opposition to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the idea of “ a consultation.” H owever, the author explicitly ascribes this 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 characterization to the Reynolds paradigm, not to Avedon’s view. Thus, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (A) confuses the passage’s inform ation. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choices (C) and (D) are qualitatively the worst choices among the five. (C) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 confuses the passage’s inform ation. The quotation in the first paragraph 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 435

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 makes it clear that Cartier-Bresson (not Avedon) conceives the encounter 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as “ confrontational.” (D) also confuses the passage’s inform ation. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 According to the passage, Avedon confesses “ uncomfortably” to his role 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 as diagnostician and psychic healer. It does not necessarily follow, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 however, that Avedon finds his encounters with his sitters to be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uncomfortable. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Q uestion 3: The correct answer is (C). Although this passage doesn’t seem 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to convey a strong central idea or thesis, the author seems to be most 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 concerned with emphasizing that a portrait sitting is a social encounter, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not just an artistic exercise, and that artists consider their relationship with 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 their sitters to be somehow significant. For this reason, (C) is a good 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 statement of the author’s main point. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) also has merit. In fact, but for (C), (A) would be the best choice 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 because it embraces the passage as a whole and properly focuses on the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author’s primary concern with exploring the relationship between artist 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and sitter. H owever, the passage does not discuss how or whether this 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relationship results in a “ successful” portrait; thus, (A) distorts the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 passage’s inform ation. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) has merit in that the author does claim that the Reynolds 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paradigm (described in the second paragraph) is “ quite different” from the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 two paradigms that the first paragraph discusses. The latter does indeed 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 involve a painter (Reynolds) whereas the other two paradigms involve 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 photographers (Cartier-Bresson and Avedon). H owever, the author does 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 not generalize from this fact that a portrait artist’s approach or view 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 depends on whether the artist is a painter or a photographer. Thus, (D) is a 2 2 12345678901234567890123456789012123456789012345678901 bit off focus and calls for an unw arranted generalization. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choices (B) and (E) are qualitatively the worst among the five choices. (B) 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 distorts the information in the passage and departs from the topic at hand. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the passage does support the notion that a portrait might reveal 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 something about the relationship between artist and sitter, the author 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 neither states nor implies that a portrait reveals anything about the artist’s 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other relationships. M oreover, nowhere in the passage does the author 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 compare portraiture with other art forms. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) is too narrow and refers to information not m entioned in the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 passage. The passage is not just about Reynolds, but about the portraiture 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 encounter in general. Also, the author does not comment on Reynold’s 2 2 12345678901234567890123456789012123456789012345678901 “ success” or about how his relationship with his sitters might have 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contributed to his success. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 436 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Techniques for Interactive Reading 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 During Step 4 of the 7-step approach you just learned, you read the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage and formulated an outline that revealed its basic structure and 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 how its ideas flowed from one to the next. In this section, we’ll focus more 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 closely on this step, which lies at the heart of GM AT Reading 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Comprehension. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Think of any GM AT reading passage as a structure of ideas. Each passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is designed to convey a number of ideas that are connected to one another 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 in some way. If you understand these ideas and the connections between 2 2 12345678901234567890123456789012123456789012345678901 them, then you truly understand the passage as a whole. Focusing on 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 structure helps you in several ways: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • It makes it easy to see the “ big picture” —what the passage is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 about as a whole. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • It tells you the purpose of the supporting details—even when you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 don’t know what those details are. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The logical structure organizes all the information in the passage, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 making it easy to locate any detail to which a particular question 2 12345678901234567890123456789012123456789012345678901 might refer. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • The structure explains how the author’s main points are related to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one another. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 It’s no coincidence that the preceding list covers just about all you’ll need 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to know to answer any of the questions the test might deal you! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Focus on the Passage’s Logical Structure 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Although GM AT passages don’t invariably have clear-cut, logical struc2 12345678901234567890123456789012123456789012345678901 tures, a structure of some kind is almost always present. H ere’s a list of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most common types of logical structures found in GM AT passages. Either 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 alone or in combination, these structures underlie most of the passages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’ll encounter on the exam. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • A theory or idea illustrated by two (or more) detailed examples or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 illustrations or supported by two (or more) arguments (the passage 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 might also critique the theory based on the examples or argu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ments) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Two (or more) alternative theories, each of which seek to explain a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 certain phenomenon (the passage might also argue for one theory 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 over another) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Pro and con arguments presented for both sides of a single issue 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 437

Part IV: Verbal A bility

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • A comparison and/or contrast between two (or more) events, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ideas, phenomena, or people 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • A cause-and-effect sequence showing how one event led to another 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (presented either in chronological order or via “ flashback,” with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 later events described before earlier ones) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • Two or three basic types, categories, or classes of a phenomenon 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 identified and distinguished, beginning with main classes, and then 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 possibly branching out to subclasses (this structure is most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 common in passages involving the natural sciences) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Each of the structures listed here scream out for paragraph breaks—to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 turn from one theory, reason, example, or class to another, or to separate 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 pros from cons or similarities from differences. But don’t assume a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 passage’s structure will reveal itself so neatly. In fact, a passage with a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 complex structure might contain only one paragraph! The moral: Use 2 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph breaks as structural clues, but don’t rely on them as crutches. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 N ow let’s look at a couple of examples. H ere’s the passage about 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 portraiture that you read earlier in this chapter. This time, key portions are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 underlined to help you see its structure. N otice how nicely it fits into the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 comparison-contrast structural pattern. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Passage 1 (comparison and contrast) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Line The encounter that a portrait records is most tangibly the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sitting itself, which may be brief or extended, collegial or 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 confrontational. Renowned photographer Cartier-Bresson has 2 12345678901234567890123456789012123456789012345678901 expressed his passion for portrait photography by characteriz2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ing it as “ a duel without rules, a delicate rape.” Such meta(5) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 phors contrast quite sharply with Richard Avedon’s conception 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of a sitting. While Cartier-Bresson reveals himself as an 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 interloper and opportunist, Avedon confesses—perhaps 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 uncomfortably—to a role as diagnostician and (by implication) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (10) psychic healer: not as someone who necessarily transforms his 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 subjects, but as someone who reveals their essential nature. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Both photographers, however, agree that the fundamental 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 dynamic in this process lies squarely in the hands of the artist. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A quite-different paradigm has its roots not in confronta12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (15) tion or consultation but in active collaboration between the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 artist and sitter. This very different kind of relationship was 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 formulated most vividly by William H azlitt in his essay entitled 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ O n Sitting for O ne’s Picture” (1823). To H azlitt, the “ bond 2 12345678901234567890123456789012123456789012345678901 2 1 of connection” between painter and sitter is most like the 2 438 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (20) relationship between two lovers. H azlitt fleshes out his thesis 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by recalling the career of Sir Joshua Reynolds. According to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H azlitt, Reynold’s sitters were meant to enjoy an atmosphere 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 that was both comfortable for them and conducive to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enterprise of the portrait painter, who was simultaneously their 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 host and their contractual employee. (25) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s a new passage. This one has a typical cause-and-effect structure. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Again, some key phrases are underlined to help reveal the structure. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 Passage 2 (cause-and-effect sequence) 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Line Scientists in the post-1917 Soviet Union occupied an ambigu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ous position—while the government encouraged and generally 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supported scientific research, it simultaneously thwarted the 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 scientific community’s ideal: freedom from geographic and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 political boundaries. A strong nationalistic emphasis on (5) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 science led at times to the dismissal of all non-Russian scien2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tific work as irrelevant to Soviet science. A 1973 article in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 L iteratunaya G azeta, a Soviet publication, insisted: “ World 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science is based upon national schools, so the weakening of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 one or another national school inevitably leads to stagnation (10) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the development of world science.” According to the Soviet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regime, socialist science was to be consistent with, and in fact 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 grow out of, the M arxism-Leninism political ideology. Toward 2 12345678901234567890123456789012123456789012345678901 2 this end, some scientific theories or fields, such as relativity 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and genetics, were abolished. Where scientific work conflicted (15) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with political criteria, the work was often disrupted. During 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the Stalinist purges of the 1930s, many Soviet scientists simply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 disappeared. In the 1970s, Soviet scientists who were part of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the refusenik movement lost their jobs and were barred from 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 access to scientific resources. N azi Germany during the 1930s (20) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and, more recently, Argentina imposed strikingly similar, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 though briefer, constraints on scientific research. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the structure of passage 2 is not quite as obvious as that of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 passage 1, the structure is nevertheless there, lying just beneath the details. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N otice that the passage’s opening describes the cause (Russia’s insular 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 political ideology), while the rest of the passage lists the effects 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 (non-Russian work was deemed irrelevant, certain theories and fields were 2 2 12345678901234567890123456789012123456789012345678901 abolished, scientific work was disrupted, and scientists disappeared). The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 final two sentences (beginning with “ in the 1970s” ) is a postscript that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 simply notes two similar cause-and-effect relationships in modern history. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 439

Part IV: Verbal A bility

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N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Look for Structural Clues, or “Triggers” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Triggers” are key words and phrases that provide clues to the structure 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and organization of the passage and the direction in which the discussion 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is flowing. The lists below contain many common trigger words and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 phrases. Be on the lookout for trigger words as you read the passage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 They’ll help you see the structure of the passage and follow the author’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 train of thought. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These words precede an item in a list (e.g., examples, classes, reasons, or 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 characteristics): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • first, second, etc. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • in addition, also, another 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These words signal that the author is contrasting two phenomena: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • alternatively, by contrast, however, on the other hand, rather than, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 while, yet 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 These words signal a logical conclusion based upon preceding material: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • consequently, in conclusion, then, thus, therefore, as a result, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accordingly 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These words signal that the author is comparing (identifying similarities 2 2 12345678901234567890123456789012123456789012345678901 between) two phenomena: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • similarly, in the same way, analogous, parallel, likewise, just as, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 also, as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These words signal evidence (factual information) used to support the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author’s argument: 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • because, since, in light of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These words signal an example of a phenomenon: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • for instance, e.g., such as, . . . is an illustration of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 O bviously, it’s not possible to circle or underline key words, or to 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 otherwise annotate passages on the CAT computer screen as you could on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the old paper-based GM AT. To help make up for this fact, the GM AT 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 test-makers shortened the length of Reading passages by about half when 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they switched to computerized testing (under the theory that a briefer 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 passage is easier to assimilate without annotating it). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 440 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The Art of Note-Taking and Outlining 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As you’re reading, make shorthand notes to summarize paragraphs or to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indicate the flow of the passage’s discussion. N otes can also help you 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 locate details more quickly and recap the passage more effectively. Keep 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your notes as brief as possible—two or three words are enough in most 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cases to indicate a particular idea or component of the passage. For 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 complicated or high-density passages, an outline is a good way to organize 2 2 12345678901234567890123456789012123456789012345678901 information and to keep particular details straight in your mind. The 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 following situations are ideal for outlining: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. If the passage categorizes or classifies various things, use an 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 outline to help you keep track of which belong in each category. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2. If the passage mentions numerous individual names (e.g., of 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 authors, artists, political figures, etc.), use notes to link them 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 according to influence, agreement or disagreement, and so forth. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 3. If the passage describes a sequence of events, use a time-line 2 12345678901234567890123456789012123456789012345678901 outline to keep track of the major features of each event in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sequence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 4. In chronological passages, mark historical benchmarks and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 divisions—centuries, years, decades, or historical periods—that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 help form the structure of the author’s discussion. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 5. Use arrows to physically connect words that signify ideas that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 link together; for example: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • To clarify cause and effect in the natural sciences or in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 context of historical events 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • To indicate who was influenced by whom in literature, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 music, psychology, etc. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • To connect names (philosophers, scientists, authors, etc.) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 with dates, events, other names, theories, or schools of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 thought, works, etc. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • To indicate the chronological order in which historical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 events occurred 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To Preview . . . or Not to Preview 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M any GM AT prep books recommend that, before reading a passage 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 straight through from beginning to end, you preview the passage by 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reading the first (and perhaps the last) sentence of each paragraph. This 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 technique supposedly provides clues about the scope of the passage, the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 1 author’s thesis or major conclusions, and the structure and flow of the 22 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 441

Part IV: Verbal A bility

www.petersons.com

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 discussion. Although these techniques make sense in theory, there are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 several reasons why in practice they are rarely helpful on the GM AT: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • O nce immersed in the passage itself, you’ll quickly forget most if 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 not all of what you learned from previewing. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • These techniques call for you to read the same material twice. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Does that sound efficient to you? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Previewing takes time—time that you might not be able to afford 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 under timed testing conditions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Previewing involves rapid vertical scrolling, which adds to eye 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 strain. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • While reading the beginning and end of each paragraph may be 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 helpful for some passages, for others this technique will be of little 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or no help—and there’s no way to know whether you’re wasting 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 your time until you’ve already wasted it. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The only situation in which you should preview is if you’re running out of 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 time. Some questions, especially the ones that refer to particular line 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 numbers, you can answer quickly by reading just one paragraph—or 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 perhaps just a few sentences. And a quick scan of the first and last few 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentences of the passage m ight provide clues about the passage’s main 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 idea or primary purpose—so you can at least take educated guesses at 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 some questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for Reading Comprehension 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 We’ve covered a lot of ground in this chapter. To help you assimilate it all, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here’s a checklist of the salient, and sage, points of advice for improving 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your reading efficiency and comprehension as you read GM AT passages. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Apply them to Part V’s practice tests, and then review them again, just 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 before exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Take Notes and (for some passages) Make 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Outlines 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 As you’re reading, make shorthand notes to summarize paragraphs or to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indicate the flow of the passage’s discussion. Keep your notes brief—just 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 enough key words to remind you of the particular idea. For complicated or 2 12345678901234567890123456789012123456789012345678901 2 high-density passages, an outline is a good way to organize information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and to keep particular details straight in your mind. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 442 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Pause Occasionally to Sum Up ad Anticipate 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 After you read each logical “ block” (perhaps after each paragraph), pause 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a moment to evaluate the paragraph as a whole. Try to recapitulate or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 summarize the paragraph as two or three basic ideas. After each 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph, answer the following questions for yourself: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 • H ow would I sum up the discussion to this point? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • At what point is the discussion now? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 • What basic points is the author trying to get across in this para2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 graph? Do these ideas continue a line of thought, or do they begin 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 a new one? 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Where is the discussion likely to go from here? 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Pay Attention to the Overall Structure of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Different types of reading passages are organized in various ways. The 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage might be organized as a chronology of events, a critique of a 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 theory, a comparison of two or more things, or a classification system. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Understanding how the passage is organized—in other words, recognizing 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 its structure—will help you articulate the passage’s main idea and primary 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 purpose, to understand the author’s purpose in mentioning various details, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and to distinguish between main points and minor details—all of which in 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 turn will help you answer the questions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Look for Structural Clues, or “Triggers” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Be on the lookout for trigger words as you read the passage. They’ll help 2 12345678901234567890123456789012123456789012345678901 you see the passage’s structure and following the author’s train of thought. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Get Bogged Down in Details 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 GM AT reading passages are packed with details: lists, statistics and other 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 numbers, dates, titles, and so forth. If you try to absorb all of the details as 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you read, you’ll not only lose sight of the main points but also lose reading 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 speed. Don’t get bogged down in the details; gloss over them. O n your 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 scratch paper, note where particular examples, lists, and other details are 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 located. Then, if a particular question involving those details is included, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you can quickly and easily locate them and read them more carefully. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 443

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Sum Up the Passage After You Read It 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 After reading the entire passage, take a few seconds to recap it. What was 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the author’s main point and what were the major supporting points? 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Remind yourself about the flow of the discussion without thinking about 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 all the details. Chances are you’ll be able to answer at least one or two of 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the questions based just on your recap. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1Don’t Bother Previewing, Unless You’re Short on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Time 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So-called “ previewing” (skimming a passage or reading just the first and 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 last few sentences of the passage) m ight allow you to make educated 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 guesses and to answer certain detail questions. But use this strategy only if 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you’re running out of time on the testing clock. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Try to Minimize Vertical Scrolling 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 You’ll need to scroll to read the entire passage. But scrolling in order to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 re-read the passage uses up valuable time, as well as creating eye strain and 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 fatigue. The best way to minimize rereading (and scrolling) is to take good 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 notes. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 444 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Take It to the N ext Level 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Welcome to the N ext Level of GM AT Reading Comprehension. H ere, 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 you’ll: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Learn how to recognize and handle the four basic, and most 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 common, types of Reading Comprehension questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Learn how to recognize and handle the less common types of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Reading Comprehension questions 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s New at the Next Level 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 H ere at the N ext Level, you’ll focus on answering the questions rather 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than on reading and understanding the passages. First, you’ll learn how to 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 recognize and handle the four most common question types: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Simple recall 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Recap 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Restatement 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Inference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To round out the chapter, you’ll learn how to identify and deal with three 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 other types of reading questions that occasionally appear on the GM AT 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (although far less frequently than the preceding ones): 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Application 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • Logical continuation 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 • M ethod 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For each of the seven question types, you’ll learn how the test-makers 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 design wrong-answer choices—and how to recognize them when you see 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 445

Part IV: Verbal A bility

www.petersons.com

N ote

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Since you’re at the N ext Level, don’t expect to encounter easy reading or 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 “ gimmee” questions in this chapter. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2345678901234567890123456789012123456789012345678901 2 1 Sample Reading Passages 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 M ost of the sample questions you’ll analyze in this chapter are based on 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 the following two passages. Go ahead and read both passages now. Also, 2 2 12345678901234567890123456789012123456789012345678901 2 earmark this page, since you’ll refer back to it throughout the chapter. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Passage 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Line The arrival of a non-indigenous plant or animal species in a 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 new location may be either intentional or unintentional. Rates 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of species movement driven by human transformations of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 natural environments as well as by human mobility—through 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 commerce, tourism, and travel—dwarf natural rates by (5) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 comparison. While geographic distributions of species natu2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 rally expand or contract over historical time intervals (tens to 2 12345678901234567890123456789012123456789012345678901 hundreds of years), species’ ranges rarely expand thousands of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 miles or across physical barriers such as oceans or mountains. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A number of factors confound quantitative evaluation of (10) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the relative importance of various entry pathways. Time lags 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 often occur between establishment of non-indigenous species 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and their detection, and tracing the pathway for a long12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 established species is difficult. Experts estimate that non2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 indigenous weeds are usually detected only after having been (15) 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 in the country for thirty years or having spread to at least ten 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 thousand acres. In addition, federal port inspection, although a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 major source of information on non-indigenous species 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 pathways, especially for agricultural pests, provides data only 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (20) when such species enter via scrutinized routes. Finally, some 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 comparisons between pathways defy quantitative analysis—for 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 example, which is more “ important” : the entry pathway of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one very harmful species or one by which many but less 12345678901234567890123456789012123456789012345678901 2 2 harmful species enter the country? 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Passage 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Line Scientists have long claimed that, in order to flourish and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 progress, their discipline requires freedom from ideological and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 geographic boundaries, including the freedom to share new 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientific knowledge with scientists throughout the world. In 2 1 2 446 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (5) the twentieth century, however, increasingly close links 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between science and national life undermined these ideals. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Although the connection facilitated large and expensive 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 projects, such as the particle-accelerator program, that would 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 have been difficult to fund through private sources, it also 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 channeled the direction of scientific research increasingly (10) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 toward national security (military defense). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For example, scientists in the post-1917 Soviet Union 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 found themselves in an ambiguous position. While the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 government encouraged and generally supported scientific 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 research, it simultaneously imposed significant restrictions on (15) 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 science and scientists. A strong nationalistic emphasis on 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science led at times to the dismissal of all non-Russian scien2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tific work as irrelevant to Soviet science. A 1973 article in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 L iteratunaya G azeta, a Soviet publication, insisted: “ World 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 science is based upon national schools, so the weakening of (20) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 one or another national school inevitably leads to stagnation 2 12345678901234567890123456789012123456789012345678901 in the development of world science.” According to the Soviet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regime, socialist science was to be consistent with, and in fact 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 grow out of, the M arxism-Leninist political ideology. Toward 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this end, some scientific theories or fields, such as relativity (25) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and genetics, were abolished. Where scientific work conflicted 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with political criteria, the work was often disrupted. During 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the Stalinist purges of the 1930s, many Soviet scientists simply 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 disappeared. In the 1970s, Soviet scientists who were part of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 the refusenik movement lost their jobs and were barred from (30) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 access to scientific resources. N azi Germany during the 1930’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and, more recently, Argentina, imposed strikingly similar, 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 though briefer, constraints on scientific research. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Simple Recall Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 For these questions, your job is to identify which answer choice provides 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information that appears in the passage and that the question asks about. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The question stem might look something like one of these: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following does the author mention as an example 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of . . .?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ According to the passage, . . . is caused by . . .?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 This is the most common question type, and it’s the easiest type because all 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that’s required to handle it is to either remember or find the appropriate 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 information in the passage. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 447

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a good example, based on passage 1 (page 446): 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 According to the passage, the rate at which plant or animal species 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 move naturally across land 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. might depend on the prevalence of animals that feed on the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. is hindered by federal port inspectors. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. is often slower than the rate at which they move across water. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. is slower than human-assisted rates. 2 12345678901234567890123456789012123456789012345678901 2 E. varies according to the size of the species. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The correct answer is D. O nly the first paragraph talks about the rate of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 species movement, so it’s there you’ll find the answer to this question. In 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lines 3–6, the author states that rates of species movement driven by 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 human transformations and mobility “ dwarf natural rates by compari- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 son.” In other words, natural rates are slower than human-assisted rates, 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 just as (D) provides. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) might be true in the “ real world,” but the passage mentions 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 nothing about predators, let alone about their affect on movement rates. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 So you can easily eliminate it. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (B) confuses the passage’s details. It refers to information in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 second paragraph, which discusses problems in determining entry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pathways. This paragraph has nothing to do with the rate of species 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 movement. Also, did you notice that (B) is a bit nonsensical? H ow could 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 port inspectors, who are located where ocean meets land, affect the rate at 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 which a species moves naturally across land? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) involves relevant information from the passage, but distorts 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that information. The last sentence in the first paragraph indicates that 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 oceans and mountains are barriers that typically prevent species move- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ment. But (C) implies that mountains pose a greater barrier than oceans. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N owhere in the passage does the author seek to compare rates across land 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with rates across water. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (E) is completely unsupported by the passage, which never 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 mentions the size of a species in any context. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 448 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In handling a Simple Recall question, don’t expect the correct answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice to quote the passage verbatim. That’s generally not how the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 test-makers write them. Instead, they prefer to paraphrase what’s in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage. In the preceding question, for instance, the precise phrase 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ human-assisted movement” doesn’t appear in the passage, does it? But 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 that’s no reason to eliminate (D), which turns out to be the correct answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choice. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N otice the types of wrong-answer ploys built into the preceding question: 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Bringing in irrelevant details from elsewhere in the passage 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • D istorting what the passage says 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Bringing in outside inform ation (not found anywhere in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage) 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 • Providing a nonsensical response to the question at hand 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These are the wrong-answer ploys you should always look for in a Simple 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Recall question. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To complicate a Simple Recall question, the test-makers might turn the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question around by asking you to identify an exception to what the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage provides (with a word such as “ except” or “ least” in upper-case 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 letters). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The author mentions all of the following as examples of . . . EXCEPT:” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ According to the passage, . . . could be caused by any of the following 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 EXCEPT:” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 To handle this variation, eliminate all choices that the passage covers and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that are relevant to the question, and you’ll be left with one choice—the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 correct one. The following question, based on passage 1 (page 446)—is a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 typical example. Although this question is about as tough a Simple Recall 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 question as you’ll find on the GM AT, you’ll probably agree that it’s pretty 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 easy. H ere it is again, along with an explanatory answer: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Whether the entry pathway for a particular non-indigenous species 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can be determined is LEAST likely to depend upon which of the 2 12345678901234567890123456789012123456789012345678901 following? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Whether the species is considered to be a pest 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Whether the species gains entry through a scrutinized route 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. The rate at which the species expands geographically 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. H ow long the species has been established 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. The size of the average member of the species 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 449

Take It to the Next Level

Tip

Chapter 11: Reading Comprehension

Part IV: Verbal A bility

www.petersons.com

Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. N owhere in the passage does the author state 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or imply that the physical size of a species’ members affects whether the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 entry pathway for the species can be determined. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 You can easily eliminate choices (B), (C), and (D). All three are mentioned 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explicitly in the second paragraph as factors affecting how precisely the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 entry pathway(s) of a species can be determined. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) is a bit trickier, and it’s the runner-up choice. Unlike the other 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 incorrect choices, (A) is not ex plicitly supported by the passage. H owever, 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the author mentions in the final paragraph that federal port inspection is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ a major source of information on non-indigenous species pathways, 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 especially for agricultural pests.” Accordingly, whether a species is an 2 2 12345678901234567890123456789012123456789012345678901 agricultural pest might have some bearing upon whether or not its entry is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 detected (by port inspectors). H ence choice (A) is not as good as choice (E), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which finds no support in the passage whatsoever. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In a tougher Simple Recall question, one wrong-answer choice will be 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 more tempting than the others because the passage will im plicitly support 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 it. Don’t be fooled; you w ill find a better choice among the five. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Recap Questions 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 For these questions, your job is to recognize either the main idea, or thesis, 2 2 12345678901234567890123456789012123456789012345678901 of the passage (or a particular paragraph) as a w hole, or the author’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 primary purpose or concern in the passage (or in a particular paragraph) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 as a w hole. In other words, you job is to recap what the passage or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph is about. The question stem will look like one of these: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following best expresses the main idea of the passage?” 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Among the following characterization, the passage is best viewed as” 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following would be the most appropriate title of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage?” 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ The author’s primary purpose in the passage [or “ in the third 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph” ] is to” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ The passage [or “in the first paragraph”] is primary concerned with” 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To handle this question type, you’ll need to recognize the passage’s (or 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 paragraph’s) overall scope and main emphasis. M ost of the wrong-answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices will fall into these categories: 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Too broad (embracing ideas outside the scope of the passage or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph) 2 1 2 450 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

Chapter 11: Reading Comprehension

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Too narrow (focusing on only a certain portion or aspect of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 discussion) 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Distorted (an inaccurate reflection of the passage’s ideas or the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author’s perspective on the topic) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To complicate a Recap question, the test-makers might include a 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 runner-up answer choice that’s just a bit off the mark. H ere’s a moderately 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficult Recap question that illustrates this tactic, along with an 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 explanatory answer: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The author’s primary purpose in the passage is to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. examine the events leading up to the suppression of the Soviet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 refusenik movement of the 1970s. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. define and dispel the notion of a national science as promul2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 gated by the post-revolution Soviet regime. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. describe specific attempts by the modern Soviet regime to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suppress scientific freedom. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. examine the major twentieth-century challenges to the norma2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tive assumption that science requires freedom and that it is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inherently international. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 E. point out the similarities and distinctions between scientific 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 freedom and scientific internationalism in the context of the 2 12345678901234567890123456789012123456789012345678901 Soviet Union. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is C. N otice that, with the exception of the very last 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sentence, the passage is entirely concerned with describing Soviet attempts 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to suppress scientific freedom. In the order mentioned, the attempts 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 include thwarting science’s ideals, emphasizing a national science, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 controlling scientific literature, and threatening and punishing renegade 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientists. Choice (C) aptly expresses this overall concern. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (D) is the runner-up. Admittedly, the passage does mention, in the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 final sentence, two other twentieth-century attempts to suppress scientific 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 freedom. H ad the passage continued by describing these two other 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 attempts, (D) would probably have been the best answer choice. But since 2 12345678901234567890123456789012123456789012345678901 it doesn’t, (D) is a bit too broad. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (A) distorts the author’s primary purpose. The author does not 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 actually discuss any specific events that might have caused the suppression 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the refusenik movement; rather, this historical phenomenon is 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 mentioned simply as another example of the Soviet regime’s long-term 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pattern of suppression. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 451

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (B) distorts the author’s perspective on the topic. Although the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author does define the concept of national science, nowhere does the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author attempt to dispel or disprove the concept. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Choice (E) distorts the author’s message and is too narrow . Although the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author does imply that scientific freedom and scientific internationalism 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 are related, the author makes no attempt to examine their differences. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 What’s more, the author’s broader concern is quite different than to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 examine the relationship between these two types of scientific freedoms. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 N ow here’s a Recap question that focuses on just one paragraph, the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 second one. An easier question would provide wrong-answer choices that 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 refer to information in the first paragraph. But this question is a bit 2 2 12345678901234567890123456789012123456789012345678901 tougher; it doesn’t allow you such an easy way to rule out wrong choices. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The second paragraph (lines 10–24) as a whole is concerned with 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. identifying the problems in assessing the relative significance of 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 various entry pathways for non-indigenous species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. describing the events usually leading to the detection of a 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 non-indigenous species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. discussing the role that time lags and geographic expansion of 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 non-indigenous species play in species detection. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. pointing out the inadequacy of the federal port inspection 2 12345678901234567890123456789012123456789012345678901 system in detecting the entry of non-indigenous species. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. explaining why it is difficult to trace the entry pathways for 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 long-established non-indigenous species 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is A. In the first sentence of the second paragraph, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the author claims that “ [a] number of factors confound quantitative 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 evaluation of the relative importance of various entry pathways.” In the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 remainder of the paragraph, the author identifies three such problems: (1) 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the difficulty of early detection, (2) the inadequacy of port inspection, and 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (3) the inherent subjectivity in determining the “ importance” of a 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 pathway. Choice (A) provides a good “ recap” of what the second 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 paragraph accomplishes. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (B) is too narrow . Although the author does mention that a species 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 is usually not detected until it spreads to at least ten-thousand acres, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author mentions this single “ event” leading to detection as part of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 broader point that the unlikelihood of early detection contributes to the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problem of quantifying the relative importance of entry pathways. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) is a distortion. Although the author mentions these factors, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 they are not “ discussed” in any detail, as (C) suggests. Also, the primary 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 concern of the second paragraph is not with identifying the factors 2 2 12345678901234567890123456789012123456789012345678901 2 1 2 452 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 11: Reading Comprehension

Take It to the Next Level

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 affecting species detection, but rather with identifying the problems in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 quantifying the relative importance of various entry pathways. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is too narrow . The author is concerned with identifying other 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 problems as well as in determining the relative importance of various entry 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 pathways. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Choice (E) is a distortion. Although the author asserts that it is difficult to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 trace an entry pathway once a species is well established, the author does 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 not explain why this is so. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The best answer to a Recap question must embrace the whole passage (or 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 paragraph) better than any other choice—while not extending beyond the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage’s scope or concerns. Look for at least one answer choice that is 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 too narrow, and at least one other that is too broad. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Restatement Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In handling a Restatement question, your job is to understand a specific 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 idea the author is trying to convey in the passage. These questions are 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 different than Simple Recall questions in that you won’t find the answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 explicitly in the text. And it’s this feature that makes them more difficult. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A Restatement question stem might look something like one of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Which of the following statements about . . . is most strongly sup2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ported by the passage’s information?” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ With which of the following statements about . . . would the author 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most likely agree?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Which of the following best characterizes . . . as viewed by . . .?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 453

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a good example of a moderately difficult Restatement question, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 based on passage 1 (page 446). N otice that the wrong-answer choices are 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 designed to confuse you by combining details from the passage that relate 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 to the question but that don’t add up. H ere’s the question again, along 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 with an explanatory answer: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Which of the following statements about species movement is best 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 supported by the passage? 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 A. Species movement is affected more by habitat modifications 2 12345678901234567890123456789012123456789012345678901 2 than by human mobility. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. H uman-driven factors affect the rate at which species move 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 more than they affect the long-term amount of such move2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ments. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. N atural expansions in the geographic distribution of spe2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 cies account for less species movement than natural contrac12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 tions do. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. N atural environments created by commerce, tourism, and 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 travel contribute significantly to species movement. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. M ovement of a species within a continent depends largely 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 upon the geographic extent of human mobility within the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 continent. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is E. This choice restates the author’s point in the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 first paragraph that rates of species, movement driven by human 2 12345678901234567890123456789012123456789012345678901 2 transformation of the natural environment and by human mobility, dwarf 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 natural rates by comparison (lines 3–6). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (A) is the most tempting wrong-answer choice. Based on the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage, habitat modifications and human mobility can both affect species 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 movement, as (A) implies. And the passage does make a comparison 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 involving human-driven species movement. So (A) looks appealing. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H owever, the comparison made in the passage is between natural species 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 movement and human-driven movement, not between human modifica- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion of habitats and human mobility. So (A) confuses the details of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (B) is easier to eliminate because it is completely unsupported by 2 2 12345678901234567890123456789012123456789012345678901 the passage, which makes no attempt to compare rate (interpreted either as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 frequency or speed) of species movement to total amounts of movement 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (distance). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) is also easier to eliminate than (A). It is completely unsupported 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 by the passage. The author makes no attempt to compare natural 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 expansions to natural contractions. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 1 2 454 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (D) is the easiest one to eliminate. You don’t even need to read the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage to recognize that (D) is a nonsensical statement. H uman mobility 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (commerce, tourism, and travel) do not create “ natural” environments. It 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 is human mobility itself, not the “ natural environment” created by it, that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 contributes significantly to species movement. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 In Reading Comprehension questions, many answer choices simply won’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 make sense, as with the nonsensical choice (D) in the preceding question. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Don’t be fooled into second-guessing yourself just because you don’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 understand what the answer choice means. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 H ere’s a good example of how the test-makers might further boost the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 difficulty level of a Restatement question. As you read this question, which 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is based on passage 2 (page 446), notice that most of the wrong answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices appear to respond to the question because they describe an 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ ambiguous position.” What’s more, most of the answer choices contain 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 information that the passage supports. The use of these two wrong-answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ploys makes this question tougher than average. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following best characterizes the “ ambiguous position” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (line 13) in which Soviet scientists were placed during the decades 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that followed the Bolshevik Revolution? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 A. The Soviet government demanded that their research result in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientific progress, although funding was insufficient to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 accomplish this goal. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 B. They were exhorted to strive toward scientific advancements, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 while at the same time the freedoms necessary to make such 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 advancements were restricted. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. While they were required to direct research entirely toward 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 military defense, most advancements in this field were being 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 made by non-Soviet scientists with whom the Soviet scientists 2 12345678901234567890123456789012123456789012345678901 2 were prohibited contact. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. They were encouraged to collaborate with Soviet colleagues 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 but were prohibited from any discourse with scientists from 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 other countries. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The Soviet government failed to identify those areas of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 research that it deemed most worthwhile, but punished those 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientists with whose work it was not satisfied. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 455

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Chapter 11: Reading Comprehension

Part IV: Verbal A bility

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Alert!

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. According to the passage, the ambiguous 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position of Soviet scientists was that the Soviet government encouraged 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 and generally supported scientific research, while at the same time 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 imposed significant restrictions upon its scientists (lines 13–16). Choice 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (B) restates this idea. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Choice (C) is the easiest one to eliminate. (C) is wholly unsupported by the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage, which neither states nor suggests either assertion made in (C), 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 which in any case does not describe an ambiguous situation. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Choice (A) is unsupported by the passage. The author neither states nor 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 suggests that the Soviets lacked sufficient funding. Although if true, (B) 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 would indicate an ambiguous position for scientists, although that 2 2 12345678901234567890123456789012123456789012345678901 ambiguity is not the kind referred to in the passage. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) is also unsupported. Although some Soviet scientists were 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 indeed punished by the government, the author neither states nor implies 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that the government failed to identify those areas of research that it 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 deemed most worthwhile. If true, (E) would indicate an ambiguous 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position for scientists; but as with choice (A), the ambiguity described in 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 (E) is not the sort referred to in the passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is the most tempting wrong-answer choice. It’s a better choice 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than either (A) or (E) because the passage supports it, at least implicitly. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 What’s more, (D), if true, would present an ambiguous position for Soviet 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientists. H owever, as with choices (A) and (E), the ambiguity that (D) 2 2 12345678901234567890123456789012123456789012345678901 describes doesn’t reflect the nature of the ambiguity referred to in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t panic when you come across a lengthy question or lengthy answer 2 2 12345678901234567890123456789012123456789012345678901 choices, as in the preceding question. Although more reading usually 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 makes for a tougher question, don’t assume you’re up against as difficult 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 a question as the preceding one. O therwise, you might give up too soon 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 on what turns out to be an easier question! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Inference Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Inference questions test your ability to recognize what the author implies, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or infers, but does not state explicitly—in other words, you are tested on 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 your ability to “ read between the lines.” To make the inference, you’ll need 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 to see a logical connection between two bits of information in the passage 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (usually in two consecutive sentences) and draw a reasonable conclusion 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 from them. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 456 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Inference questions resemble Critical Reading questions in that to answer 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 them, you need to distinguish a reasonable, well-supported conclusion 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 from unreasonable, poorly supported ones. But don’t expect them to look 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exactly the same or require the same level of inferential reasoning as 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Critical Reading questions. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Look for two basic types of Inference questions on the GM AT. O ne type 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 focuses just on the passage’s ideas. Your job is to infer a specific idea from 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 what’s stated. The question stem will probably contain some form of the 2 2 12345678901234567890123456789012123456789012345678901 word “ infer,” as in these two examples: 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 “ It can be inferred from the passage that the reason for . . . is that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 . . .” 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The discussion about . . . most reasonably infers which of the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 following?” 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A second type of Inference question asks you to infer the author’s purpose 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in mentioning a specific idea. Look for a question stem like one of these: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The author mentions . . . (lines X-X) most probably in order to” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ The example discussed in lines X-X is probably intended to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 illustrate” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 In designing either type of Inference question, the test-makers will often in- 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 clude a runner-up answer choice in which the inference is a bit more specu- 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 lative than the inference in the best choice. Both of the following questions, 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 based on passage 2 (page 446) incorporate this wrong-answer ploy. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Which of the following is most reasonably inferable from the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage’s first paragraph (lines 1–11)? 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. Expensive research projects such as the particle-accelerator 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 program apply technology that can also be applied toward 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 projects relating to national security. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. Scientific knowledge had become so closely linked with 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 national security that it could no longer be communicated to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 scientific colleagues without restriction. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 C. Without free access to new scientific knowledge, scientists in dif2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 ferent countries are less able to communicate with one another. 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 D. Governments should de-emphasize scientific projects related to 2 12345678901234567890123456789012123456789012345678901 military defense and emphasize instead research that can be 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 shared freely within the international scientific community. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. Government funding of scientific research undermines the ideal 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 of scientific freedom to a greater extent than private funding. 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 457

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Chapter 11: Reading Comprehension

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is B. The first two sentences establish that the link 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between science and national life undermined scientists’ freedom to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 communicate with other scientists. The next sentence points to the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 channeling of scientific research toward protecting national security as a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 manifestation of that link. N otice the almost unavoidable inference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 here—that national security concerns were part of the “ national life” that 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 took precedence over scientific freedoms. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (E) is the runner up. An argument can be made from the 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 information in the first paragraph that government-funded research is 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 more likely than privately-funded research to relate to matters affecting 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 the national security (i.e., military defense). H owever, this inference is 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 hardly as unavoidable as the one that (B) provides, is it? To compete with 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 (B), the inference would need additional supporting evidence. 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (A) is unsupported. The author implies no connection between the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 particle-accelerator program and national security. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (C) is nonsensical. Ready access to new scientific knowledge would 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 require ready communication among scientists—not the other way around. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is unsupported. The author neither states nor suggests which 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 areas of scientific research should be emphasized. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The author quotes an article from L iteratunaya G azeta (lines 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 19–22) most probably in order to 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. illustrate the general sentiment among members of the interna2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tional scientific community during the time period. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 B. support the point that only those notions about science that 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 conformed to the M arxist-Leninist ideal were sanctioned by 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 the Soviet government. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. show the disparity of views within the Soviet intellectual 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 community regarding the proper role of science. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. underscore the Soviet emphasis on the notion of a national 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. support the author’s assertion that the M arxist-Leninist impact 2 2 12345678901234567890123456789012123456789012345678901 on Soviet scientific freedom continued through the decade of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the 1970s. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is D. This part of the passage is concerned 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 exclusively with pointing out evidence of the Soviet emphasis on a national 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science; given the content of the excerpt from L iteratunaya G azeta, you 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can reasonably infer that the author is quoting this article as one such piece 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 of evidence. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 458 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 11: Reading Comprehension

Take It to the Next Level

Tip

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Choice (A) is easy to rule out because it distorts the nature of the quoted 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 article and runs contrary to the passage. The article illustrates the official 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Soviet position and possibly the sentiment among some members of the 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 Soviet intellectual or scientific community. H owever, the article does not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 necessarily reflect the views of scientists from other countries. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 Choice (C) is not likely to be the author’s purpose in quoting the article, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 because the author does not discuss disagreement and debate among 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Soviet intellectuals. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Choice (E) is a bit tempting because it might in fact be true and because it 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 is indeed supported by the information in the passage. But the author gives 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 no indication as to when the article was written or published; thus, the 2 2 12345678901234567890123456789012123456789012345678901 article itself lends no support to (E). 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (B) is the runner-up choice that helps make this question tougher 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than it would be otherwise. The quoted article does indeed reflect the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M arxist-Leninist ideal (at least as interpreted and promulgated by the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 government) and may in fact have been published only because it was 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 sanctioned (approved) by the Soviet government. H owever, since this 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 conclusion would require speculation, and since the quoted excerpt makes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 no mention of government approval or disapproval of certain scientific 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 notions, it is not likely that (B) expresses the author’s purpose in quoting 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the article. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 When handling Inference questions, you need to know the difference 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between a reasonable inference, which no rational person could dispute 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 based on the passage’s information, and mere speculation, which requires 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 additional information to hold water. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Method Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 M ethod questions ask you to recognize how the author goes about making 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 his points—rather than focusing on the points themselves. Some M ethod 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 questions ask for the author’s overall approach in the passage, while 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 others ask about how a specific point is made or about the structure of a 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 particular paragraph. In M ethod questions, the answer choices are usually 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 stated very generally, and it’s up to you to connect the general wording of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the choices with what’s going on in the passage. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A M ethod question can appear in many different forms. H ere are just a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 few examples of what the question stem might look like: 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ Which of the following best describes the approach of the passage?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 “ In the last paragraph (lines X-X), the author proceeds by” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 459

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 “ H ow does the second paragraph function in relation to the first 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following most accurately describes the organization of 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the second paragraph (lines X-X)?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following techniques is used in the second paragraph 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 (lines X-X)?” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 When you see a M ethod question, first let the question guide you to the 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 appropriate area of the passage. Your notes or outline might suffice to 2 2 12345678901234567890123456789012123456789012345678901 determine how the author proceeds in making her points there. If not, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reread that section carefully. Focus on what the author is doing; don’t get 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 bogged down in details. Again, M ethod questions concern how the author 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 makes points, not what those points are. 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the last paragraph of a passage about Francis Bacon, a sixteenth- 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 century philosopher of science. (As a whole, the passage explores the link 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 between his thinking and the modern-day scientific establishment.) Read 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the paragraph, then answer the M ethod question based on it. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Line N o one questions the immense benefits already conferred by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 science’s efficient methodology. H owever, since individual 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 scientists must now choose between improving standards of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 living and obtaining financial support for their research, there 2 12345678901234567890123456789012123456789012345678901 is cause for concern. In light of current circumstances, we must 2 (5) 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ask certain questions about science that Francis Bacon, from a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sixteenth-century perspective, could not possibly have put to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 himself. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Which of the following most accurately describes the technique that 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the author employs in the last paragraph of the passage? 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. An assertion is made and is backed up by evidence. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. A viewpoint is expressed and an opposing viewpoint is stated 2 12345678901234567890123456789012123456789012345678901 and countered. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. An admission is offered and is followed by a warning and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 recommendation. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 D. Contradictory claims are presented and then reconciled. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. A problem is outlined and a solution is proposed and defended. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 460 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 11: Reading Comprehension

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. The notion that no one questions the benefits 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of science does qualify as an admission in the context of the paragraph; 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 that is, the author admits that science has given mankind enormous 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 benefits. The author then goes on to voice his concern regarding the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 current state of the scientific enterprise. N ote how the contrast signal word 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ however” flags us that some kind of change must come after the author 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 admits that science has conferred immense benefits. Indeed, what comes 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 next is, as (C) puts it, a warning: there is cause for concern. A 2 2 12345678901234567890123456789012123456789012345678901 recommendation appears in the final sentence, highlighted by the words 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ we must ask certain questions. . . .” Every element in (C) is present and 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 accounted for, so (C) aptly describes the technique used in the paragraph. 2 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 Choice (A) indicates that the paragraph begins with an assertion, and we 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 can surely accept that: the assertion that no one questions the benefits of 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 science. Is this then backed up by evidence? N o. The contrast signal word 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 “ however” tells us that some kind of change is coming, but does not 2 2 12345678901234567890123456789012123456789012345678901 provide evidence for the statement in the first sentence. And indeed, the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph does go in a different direction. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (B) doesn’t reflect what’s going on in the paragraph. (B) claims that 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the final paragraph begins with a viewpoint, which it does. But does an 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 opposing viewpoint follow—that is, an argument against the benefits of 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 science? N o; instead, concern is expressed about the way science is now 2 12345678901234567890123456789012123456789012345678901 conducted. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (D) is incorrect because there are no contradictory claims here. The 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 author admits that science has given humankind enormous benefits, but 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 then goes on to voice his concern regarding the current state of the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 scientific enterprise. These things aren’t contradictory, and nothing in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 paragraph reconciles them, so (D) can’t be the best choice. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 As for (E), it’s fair to say that a problem is outlined. (The problem is that 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 securing financial support for scientific work might get in the way of 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 scientists improving standards of living.) But does the author propose a 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 solution? N o. H e recommends that serious questions be asked about the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 problem, but offers no solution of his own. Besides, the passage ends 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 before any kind of defense of his recommendation is offered. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 461

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Application Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 These questions, which require you to apply the author’s ideas to new 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 situations, usually involve relatively broad inferences. You might be asked 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 to interpret how the author’s ideas apply to, or are affected by, other 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 situations. To do this requires you to make logical connections between the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 author’s stated ideas and other ideas not explicitly discussed in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage. O r, you might be asked to assess the author’s attitude (agreement 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 or disagreement) toward some new situation. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 Application questions often add or refer to new information, so there’s no 2 2 12345678901234567890123456789012123456789012345678901 predictable question stem to look for. But, the stem might look something 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 1 like one of these three: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ If it were determined that __________, what effect would this fact 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 have on the author’s assessment of __________ as presented in the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following new discoveries, if it were to occur, would 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 most strongly support the author’s theory about __________ ?” 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 “ Which of the following is most analogous to the situation of 2 2 12345678901234567890123456789012123456789012345678901 __________ described in the passage?” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In dealing with Application questions: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Be on the lookout for wrong-answer choices that require you to 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 make an inference not supported by the passage. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Eliminate answer choices that contradict the author’s main idea or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 position. 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Eliminate answer choices that distort the passage’s ideas. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s another brief excerpt from a passage about Francis Bacon (the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sixteenth-century philosopher of science), along with an Application 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 question based on the excerpt. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Line Francis Bacon contributed to the scientific enterprise a 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 prophetic understanding of how science would one day be put 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 to use in the service of technology and how this symbiotic 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 relationship between the two would radically impact both man 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 and his surroundings. As inseparable as they are today, it is (5) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 hard to imagine science and technology as inhabiting separate 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 domains. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 462 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 11: Reading Comprehension

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 As discussed in the passage, the relationship between science and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 technology is best illustrated by which of the following scenarios? 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 A. A biologist writes an article documenting a new strain of 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 influenza that is subsequently published and taught in medical 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 schools around the world 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 B. A breakthrough in the field of psychology enables psychoana2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 lysts to diagnose patients with greater accuracy 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. An engineering firm hires a public relations agency to advertise 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 the benefits of a labor-saving mechanical device 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 D. A physics discovery leads to the development of a machine that 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 helps researchers view previously uncharted areas of the ocean 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 floor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 E. The development of a new software application that helps 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 research scientists isolate genes that are responsible for certain 2 12345678901234567890123456789012123456789012345678901 diseases 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 The correct answer is D. If you’re not sure what “ symbiotic” means, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 you can figure it out by its context. We’re told that science is used to help 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 develop and contribute to technology, and that technology also contrib12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 utes to science. So we need to find the choice that illustrates the same sort 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 of link. (D) fits the bill: A scientific discovery in one area (physics) leads to 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 the invention of a technology (a machine) that helps scientists in another 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 field (oceanography) make new discoveries. The interplay between science 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 and technology in this example is a good application of the author’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 description of “ symbiotic relationship.” 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 N ether (A) nor (B) account for technology; they involve only science. Since 2 12345678901234567890123456789012123456789012345678901 there’s nothing in either choice about the interplay between science and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 technology, neither is as good a choice as (D). 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 As for (C), if there’s a symbiotic relationship at work at all in (C), it’s 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 between technology (a new mechanical device) and marketing. There’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 nothing about science here, so this choice doesn’t illustrate the interplay 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 between science and technology. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (E) is the runner-up choice. It illustrates how science (genetic 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 research) can benefit from technology (a computer application). But it 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 does not illustrate the reverse relationship—how technology can also 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 benefit from science. So (E) does not illustrate as completely as (D) the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 symbiotic relationship the author describes. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 463

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Logical Continuation Questions 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In this question type, the test-maker gauges your ability to determine the 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 flow of the discussion and anticipate where it will go beyond the end of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage—were the passage to continue. A Logical Continuation question 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 stem might look something like one of the following: 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 “ Which of the following would be the most logical continuation of the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 passage?” 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 “ The author would probably continue the discussion by” 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To answer a question of this type, it helps to have a general outline of the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 passage so that you know how it flows and therefore how it would 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 continue to flow. H owever, just the final few sentences probably provide 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 enough information for you to eliminate some of the wrong-answer 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 choices—and possibly even zero-in on the best choice. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 In dealing with Logical Continuation questions: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 • Focus on the operative word (probably the first word) in each 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer choice. This can help you narrow down the choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 • Be on the lookout for wrong-answer choices that rehash what’s 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 already been covered in the passage. Although the discussion is 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 unlikely to reverse course, don’t automatically rule out this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 possibility. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H ere’s the final paragraph of a passage about the geography of a South 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 American mountain range. Based only on this paragraph, you can narrow 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 down the choices—and probably even hone-in on the best one! 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Line At the regional or macroscale level, vegetation patterns in the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 N orthern and Central Andes tend to reflect climatic zones 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 determined by latitude and altitude. At the local or mesoscale, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 however, this correspondence becomes less precise, as local 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 variations in soil type, slope, drainage, climate, and human (5) 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 intervention come into play. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 464 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

www.petersons.com

Chapter 11: Reading Comprehension

Alert!

Take It to the Next Level

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Among the following, the passage would most logically continue by 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 A. describing the climate and topography of the portions of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Andean cordillera other than the N orthern and Central 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 regions. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 B. discussing how highand low-pressure systems affect the 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 climate of the Amazon. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 C. exploring how proximity to the equator affects vegetation in 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the Andean cordillera. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 D. identifying problems in determining the relation between soil 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 type and vegetation in the Andean cordillera. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 E. examining the effects of vegetation patterns on the topography 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 of the Andean cordillera. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The correct answer is C. In the final paragraph, the author asserts that 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 altitude as well as latitude (proximity to the equator) determine climatic 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 zones as reflected by vegetation patterns. Accordingly, a more detailed 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 discussion about why different forms of vegetation appear at different 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 latitudes is a logical continuation. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Choice (D) is the runner-up choice; it’s consistent with the content of the 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 final paragraph, and the author does suggest a relationship between soil 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 type and vegetation (presumably, soil type determines what forms of 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 vegetation will thrive). H owever, the paragraph neither indicates nor 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 suggests any potential problems in determining such a relationship. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 Choices (A) and (B) both ignore the direction of the final paragraph. 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 Choice (E) appears at first glance to be a viable answer because it 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 includes the same subject matter (i.e., vegetation) as the final paragraph. 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 H owever, (E) is a bit nonsensical—it is unlikely that vegetation would 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 have much effect upon topography; even if it did, nothing in the final 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 paragraph indicates that this is the direction in which the discussion is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 likely to turn. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 In handling a Logical Continuation question, the passage’s final few 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 sentences are sure to help you narrow down the answer choices. But, by 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 all means, don’t ignore the rest of the passage! Check your notes or 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 outline for the flow of ideas from the passage’s beginning to its end. The 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 best answer choice should go with the overall flow. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 465

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 The Test-Makers’ Top 10 Wrong-Answer Ploys 22 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 If you read the analysis of each sample question in this chapter carefully, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you learned a lot about how the test-makers design wrong-answer choices. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 N ow here’s a review of the types they resort to most often: 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 1. The response distorts the information in the passage. It might 2345678901234567890123456789012123456789012345678901 2 1 12345678901234567890123456789012123456789012345678901 understate, overstate, or twist the passage’s information or the 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 author’s point in presenting that information. 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 2. The response uses information from the passage, but does not 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 answer the question. The information cited from the passage isn’t 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 useful to respond to the question at hand. 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 3. The response relies on speculation or an unsupported inference. It 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 calls for some measure of speculation in that the statement is not 2 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 readily inferable from the information given. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 4. The response is contrary to what the passage says. It contradicts the 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 passage’s information or runs contrary to what the passage infers. 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 5. The response gets something in the passage backwards. It 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 reverses the logic of an idea in the passage, confuses cause with 2 2 12345678901234567890123456789012123456789012345678901 effect, or otherwise turns information in the passage around. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 6. The response confuses one opinion or position with another. It 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 incorrectly represents the viewpoint of one person (or group) as 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 that of another. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 7. The response is too narrow or specific. It focuses on particular 2 2 12345678901234567890123456789012123456789012345678901 information in the passage that is too specific or narrowly 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 focused in terms of the question posed. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 8. The response is too broad (general). It embraces information or 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 ideas that are too general or widely focused in terms of the 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 question posed. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 9. The response relies on information that the passage does not men- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tion. It brings in information not found anywhere in the passage. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10. The response is utter nonsense. It makes almost no logical sense 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 in the context of the question; it’s essentially gibberish. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 466 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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Chapter 11: Reading Comprehension

Take It to the Next Level

X-Ref

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Success Keys for Answering Reading 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Comprehension Questions 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 H ere’s a checklist of tips for answering Reading Comprehension ques- 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 tions. Some of these tips reiterate suggestions made earlier in this 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 chapter—suggestions that are worth underscoring—while others are new 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 here. Apply these points of advice to Part V’s practice tests, and then 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 review them again, just before exam day. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Second-Guess the Test-Maker 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 1 The directions for the GM AT Reading Comprehension sets instruct you to 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choose the “ best” among the five answer choices. Isn’t this awfully 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 subjective? True, there is an element of subjective judgment involved in 2 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 reading comprehension. H owever, these questions are reviewed, tested, 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 and revised several times before they appear as scored questions on an 2 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 actual GM AT. If you think there are two or more viable “ best” choices, 2 12345678901234567890123456789012123456789012345678901 you (not the test-maker) have either misread or misinterpreted the passage, 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the question, or the answer choices. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Read Each and Every Answer Choice in its 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Entirety 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 As you know, you’re looking for the “ best” answer choice. O ften, more 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 than one choice will be viable. Don’t hastily select or eliminate answer 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 choices without reading them all. G M AT testtak ers m iss m ore questions 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 for this reason than for any other! 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 If you read the beginning of this chapter, you already know that you 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 should never confirm your selection for any question until you’ve read the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 entire passage—even if the first few questions seem clearly to involve the 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 initial portion of the passage. It’s always possible that information 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 relevant to these questions will appear at the end of the passage. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Don’t Over-Analyze Questions or Second-Guess 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Yourself 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 If you believe you understood the passage fairly well, but a particular 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 answer choice seems confusing or a bit nonsensical, do not assume that it’s 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 your fault. M any wrong-answer choices simply don’t make much sense. If 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 an answer choice strikes you this way, don’t examine it further; eliminate 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 it. Similarly, if you’ve read and considered all five choices, and one strikes 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 you as the best one, m ore often than not, your initial hunch w ill be correct. 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 467

Part IV: Verbal A bility

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Don’t Overlook the Obvious 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Reading Comprehension questions vary in difficulty level, and this means 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 that many of the questions are rather easy. If a particular choice seems 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 obviously correct or incorrect, don’t assume that you are missing 2 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 something. You might simply have come across a relatively easy question. 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Eliminate Answer Choices that Run Contrary to 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1the Main Idea 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Regardless of the type of question you are dealing with, keep in mind the 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 overall thesis, main idea, or point that the author is making in the passage 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 as a whole. Any answer choice to any question that runs contrary to or is 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 inconsistent with that thesis can be eliminated. You may be surprised how 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 many questions can be answered correctly using only this guideline. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Be Alert to the Test-Makers’ Favorite Wrong2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Answer Ploys 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Keep a mental list of the wrong-answer types or ploys you learned about in 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 this chapter. When you have trouble narrowing down the answer choices, 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 review this list in your mind, and the remaining wrong answers should 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 reveal themselves. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 468 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012

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PART

V Three Practice Tests Practice Test 1

470

Answers and Explanations Practice Test 2

512

Answers and Explanations Practice Test 3

497

537

553

Answers and Explanations

577

PART V

Practice Test

1 1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Analysis of an Issue 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 Question—30 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose a response to the following statement and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 “ As adults we prefer to define ourselves more by our occupation than by our affiliation with 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 social groups.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 In your view, how accurate is the foregoing statement? Use reasons and/or examples from your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 experience, observation, and/or reading to explain your viewpoint. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 Question—30 Minutes 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose an essay for the following argument and 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The following appeared as part of an article in a national business publication: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 “ Workforce Systems, a consulting firm specializing in workplace productivity and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 efficiency, reports that nearly seventy percent of M axtech’s employees who enrolled in 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Workforce Systems’ one-week seminar last year claim to be more content with their current 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 jobs than prior to enrolling in the seminar. By requiring managers at all large corporations 6 6 123456789012345678901234567890121234567890123456789012345678901212345 to enroll in the kinds of seminars that Workforce System offers, productivity in our 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 economy’s private sector is certain to improve.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 line of reasoning and the use of evidence in the argument. For example, you may need to 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 470

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 consider what questionable assumptions underlie the thinking and what alternative explana- 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tions or counterexamples might weaken the conclusion. You can also discuss what sort of 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 evidence would strengthen or refute the argument, what changes in the argument would make 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 it more logically sound, and what, if anything, would help you better evaluate its conclusion. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Quantitatiave Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 37 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Problem Solving Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 screen before your first Problem Solving question.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Solve this problem and indicate the best of the answer choices given. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 N umbers: All numbers used are real numbers. 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Problem Solving question is intended to provide infor6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 mation useful in solving the problem. Figures are drawn as accurately as possible EXCEPT 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 when it is stated in a specific problem that its figure is not drawn to scale. Straight lines 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 may sometimes appear jagged. All figures lie on a plane unless otherwise indicated. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Data Sufficiency Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first D ata Sufficiency question.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 This Data Sufficiency problem consists of a question and two statement, labeled (1) and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2), in which certain data are given. You have to decide whether the data given in the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 statements are sufficient for answering the question. Using the data given in the statements 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 plus your knowledge of mathematics and everyday facts (such as the number of days in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 July or the meaning of counterclock w ise), you must indicate whether: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statement (1) ALO N E is sufficient, but statement (2) alone is not sufficient to answer 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) ALO N E is sufficient, but statement (1) alone is not sufficient to answer 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 BO TH statements (1) and (2) TO GETH ER are sufficient to answer the question asked; 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 but N EITH ER statement ALO N E is sufficient; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 EACH statement ALO N E is sufficient to answer the question asked; 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statements (1) and (2) TO GETH ER are N O T sufficient to answer the question asked, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and additional data specific to the problem are needed. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 471

Part V: T hree Practice Tests

N ote

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N umbers: All numbers used are real numbers. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Data Sufficiency problem will conform to the informa6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tion given in the question, but will not necessarily conform to the additional information 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in statements (1) and (2). 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Lines shown as straight can be assumed to be straight and lines that appear jagged can also 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be assumed to be straight. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 You may assume that positions of points, angles, regions, etc., exist in the order shown and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that angle measures are greater than zero. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 All figures lie in a plane unless otherwise indicated. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N ote: In Data Sufficiency problems that ask you for the value of a quantity, the data given 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in the statements are sufficient only when it is possible to determine exactly one numerical 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 value for the quantity. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Although the questions in this section cover all difficulty levels, you’ll find fewer easy 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 questions than challenging ones. Keep in mind that the GM AT CAT will determine the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 difficulty level of each question based on your responses to prior questions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 3 2 6 123456789012345678901234567890121234567890123456789012345678901212345 1. 4 1 3 2 2 5 2. Lyle’s current age is 23 years, and 6 123456789012345678901234567890121234567890123456789012345678901212345 2 4 5 6 123456789012345678901234567890121234567890123456789012345678901212345 M elanie’s current age is 15 years. H ow 6 123456789012345678901234567890121234567890123456789012345678901212345 many years ago was Lyle’s age twice 6 123456789012345678901234567890121234567890123456789012345678901212345 29 6 123456789012345678901234567890121234567890123456789012345678901212345 A. M elanie’s age? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 5 6 123456789012345678901234567890121234567890123456789012345678901212345 23 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 7 B. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4 C. 8 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 9 117 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 16 6 123456789012345678901234567890121234567890123456789012345678901212345 20 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 231 6 123456789012345678901234567890121234567890123456789012345678901212345 3. If x and y are integers, is x 1 y 2 1 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 40 6 divisible by 3? 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 57 (1) When x is divided by 3, the remainder 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 is 2. 10 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) When y is divided by 6, the remainder 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is 5. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 472 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 7. 4. Four knots—A , B, C, and D —appear in 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that order along a straight length of rope. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Is the distance between B and D the same 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 as the distance between A and B? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) The distance between A and C is less 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 than the distance between B and D 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) H alf the distance between A and D is 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 the same as the distance between C 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and D . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 5. Is x . y ? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 According to the chart shown above, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) x is the arithmetic mean of all 3456789012345678901234567890121234567890123456789012345678901212345 6 12 during the year that Country X’s exports 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 two-digit prime numbers less than 23. 6 123456789012345678901234567890121234567890123456789012345678901212345 exceeded its own imports by the greatest 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) y is the sum of all factors of 60 that dollar amount, Country Y’s imports 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 are greater than 21 but less than 6. exceeded Country X’s imports by approxi- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 mately 6 123456789012345678901234567890121234567890123456789012345678901212345 6. In a boat race between David and Jeff, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. $23 billion. when Jeff had covered half the 30-mile 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. $75 billion. race distance, David was two miles ahead 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. $90 billion. of Jeff. H ow long did it take David to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. $110 billion. travel the entire 30-mile distance? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. $160 billion. 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) David traveled the last 15 miles of the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 race’s distance in 40 minutes. 8. A certain zoo charges exactly twice as 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 much for an adult admission ticket as for 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) Jeff traveled the first 15 miles of the 6 123456789012345678901234567890121234567890123456789012345678901212345 a child’s admission ticket. If the total race’s distance in 45 minutes. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 admission price for the family of two 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 adults and two children is $12.60, what is 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the price of a child’s ticket? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. $1.60 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. $2.10 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. $3.20 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. $3.30 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. $4.20 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 473

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 12. If (bNaNc) 5 ab 2 c, then 9. If n is the first of two consecutive odd 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (4N3N5) 1 (6N5N7) 5 integers, and if the difference of their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 squares is 120, which of the following 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 equations can be used to find their values? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 11 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 15 A. (n 1 1) 2 n 5 120 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. 30 B. n 2 (n12) 5 120 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 40 C. [(n 1 2) 2 n] 5 120 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 D. n 2 (n 1 1) 5 120 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 13. Two competitors battle each other in each E. (n 1 2) 2 n 5 120 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 match of a tournament with nine partici- 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 pants. What is the minimum number of 10. M is P% of what number? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 matches that must occur for every 3456789012345678901234567890121234567890123456789012345678901212345 6 12 MP 3456789012345678901234567890121234567890123456789012345678901212345 6 12 competitor to battle every other competiA. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 100 tor? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 100P 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 27 B. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 M B. 36 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 45 M 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 64 6 123456789012345678901234567890121234567890123456789012345678901212345 100P 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 81 6 123456789012345678901234567890121234567890123456789012345678901212345 P 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 14. What is the value of x ? 100M 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 100M (1) 4x 2 2 4x 5 21 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 P 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) 2x 1 9x 5 5 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 11. 6 123456789012345678901234567890121234567890123456789012345678901212345 2y y 2 1 6 123456789012345678901234567890121234567890123456789012345678901212345 15. If, 5 then y 5 6 123456789012345678901234567890121234567890123456789012345678901212345 9 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Three carpet pieces—in the shapes of a 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 square, a triangle, and a semicircle—are 3 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 6 123456789012345678901234567890121234567890123456789012345678901212345 attached to one another, as shown in the 6 123456789012345678901234567890121234567890123456789012345678901212345 5 6 123456789012345678901234567890121234567890123456789012345678901212345 figure above, to cover the floor of a room. 6 123456789012345678901234567890121234567890123456789012345678901212345 4 If the area of the square is 144 feet and the 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 perimeter of the triangle is 28 feet, what is 6 123456789012345678901234567890121234567890123456789012345678901212345 9 6 123456789012345678901234567890121234567890123456789012345678901212345 the perimeter of the room’s floor, in feet? 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 2 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 32 1 12p 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 40 1 6p 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 3 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 34 1 12p 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 52 1 6p 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 52 1 12p 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 1 6 474 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 19. Barbara invests $2,400 in the N ational 16. A 30-ounce pitcher is currently filled to 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Bank at 5% . H ow much additional money 6 exactly half its capacity with a lemonade 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 must she invest at 8% so that the total mixture consisting of equal amounts of 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 annual income will be equal to 6% of her 6 two lemonade brands—A and B. If the 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 entire investment? pitcher is then filled to capacity to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 conform to a certain recipe, how many 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 A. $1,200 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ounces of each lemonade brand must be 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. $3,000 3456789012345678901234567890121234567890123456789012345678901212345 6 12 added to fill the pitcher? 6 123456789012345678901234567890121234567890123456789012345678901212345 C. $1,000 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. $3,600 (1) The recipe calls for a mixture that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. $2,400 includes 60 percent brand A. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) When filled to capacity, the pitcher 20. ABC Company pays an average of $140 3456789012345678901234567890121234567890123456789012345678901212345 6 12 contains 12 ounces of brand B. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 per vehicle each month in outdoor parking 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fees for three of its eight vehicles. The 6 123456789012345678901234567890121234567890123456789012345678901212345 17. Lisa has 45 coins, which are worth a total 6 123456789012345678901234567890121234567890123456789012345678901212345 company pays garage parking fees for the 6 123456789012345678901234567890121234567890123456789012345678901212345 of $3.50. If the coins are all nickels and 6 123456789012345678901234567890121234567890123456789012345678901212345 remaining five vehicles. If ABC pays an 6 123456789012345678901234567890121234567890123456789012345678901212345 dimes, what is the difference between the 6 123456789012345678901234567890121234567890123456789012345678901212345 average of $240 per vehicle overall each 6 123456789012345678901234567890121234567890123456789012345678901212345 number of nickels and the number of 6 123456789012345678901234567890121234567890123456789012345678901212345 month for parking, how much does ABC 6 123456789012345678901234567890121234567890123456789012345678901212345 dimes? 6 123456789012345678901234567890121234567890123456789012345678901212345 pay per month in garage parking fees for 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 5 its vehicles? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. 10 6 123456789012345678901234567890121234567890123456789012345678901212345 A. $300 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 15 6 123456789012345678901234567890121234567890123456789012345678901212345 B. $420 D. 20 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. $912 E. 25 123456789012345678901234567890121234567890123456789012345678901212345 66 D. $1,420 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. $1,500 6 123456789012345678901234567890121234567890123456789012345678901212345 18. In an election between two candidates— 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Lange and Sobel—70% of the voters 123456789012345678901234567890121234567890123456789012345678901212345 21. If m 5 n and p , q, which of the follow- 6 6 123456789012345678901234567890121234567890123456789012345678901212345 voted for Sobel. O f the election’s voters, 6 123456789012345678901234567890121234567890123456789012345678901212345 ing must be true? 6 123456789012345678901234567890121234567890123456789012345678901212345 60% were male. If 35% of the female 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. m 2 p . n 2 q voters voted for Lange, what percentage 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. p 2 m . q 2 n of the male voters voted for Sobel? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. m 2 p , n 2 q A. 14 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. m p . nq B. 16 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. m 1 q , n1 p C. 26 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 44 6 123456789012345678901234567890121234567890123456789012345678901212345 c c 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 65 22. If ab Þ 0, is . ? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a b 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) c Þ 0 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) a . b 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 475

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 23. If the price of a candy bar is doubled, by 27. If x y , 0, and if x and y are both integers, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 what percent will sales of the candy bar what is the difference in value between x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 decrease? and y? 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) For every ten cent increase in price, (1) x 1 y 5 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the sales will decease by 5 percent. 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) 23 , x , y 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) Each candy bar now costs sixty cents. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 7 6 123456789012345678901234567890121234567890123456789012345678901212345 28. A photographic negative measures 1 24. What is the numerical value of the second 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 8 3456789012345678901234567890121234567890123456789012345678901212345 6 12 term in the following sequence: x , x 1 1, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 inches. If the longer side of inches by 2 x 1 3, x 1 6, x 1 10, x 1 15, . . .? 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 the printed picture is to be 4 inches, what 6 (1) The sum of the first and second terms 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 will be the length of the shorter side of the 6 is one-half the sum of the third and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 printed picture? fourth terms. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) The sum of the sixth and seventh 3 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 2 inches 6 123456789012345678901234567890121234567890123456789012345678901212345 terms is 43. 6 123456789012345678901234567890121234567890123456789012345678901212345 8 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 25. O n the x y-plane, what is the area of a 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 2 inches 6 123456789012345678901234567890121234567890123456789012345678901212345 right triangle, one side of which is defined 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 by the two points having the (x ,y) 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 C. coordinates (2,3) and (24,0)? 2 inches 123456789012345678901234567890121234567890123456789012345678901212345 66 4 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) The triangle’s perimeter crosses the 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 3 inches 6 123456789012345678901234567890121234567890123456789012345678901212345 y-axis at exactly two points altogether. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) The y-coordinate of two of the E. 3 inches 6 123456789012345678901234567890121234567890123456789012345678901212345 8 6 123456789012345678901234567890121234567890123456789012345678901212345 triangle’s three vertices is 0 (zero). 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 26. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 In the figure above, what is the value of x ? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) y 5 130 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) z 5 100 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 476 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 30 and 31 refer to the following 29. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 figure: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 6 123456789012345678901234567890121234567890123456789012345678901212345 If the circumference of the circle pictured 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 above is 16p, what is the length of A C? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 4 =2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 16 6 123456789012345678901234567890121234567890123456789012345678901212345 30. With respect to the two-month period 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 123456789012345678901234567890121234567890123456789012345678901212345 16 =2 over which the average daily temperature 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 32 in City X increased by the greatest 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 16p percentage, City Y’s average daily 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 temperature was approximately 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 38 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 42 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 52 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 64 degrees. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 68 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 31. During the time periods in which City Y’s 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 average daily temperature was increasing 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 while City X’s was decreasing, the average 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 daily temperature in City Y exceeded that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in City X by approximately 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 0 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 4 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 10 degrees. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 15 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 19 degrees. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 477

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 y2 y2 34. 32. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 18 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 0 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2y 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 3 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 19y 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 y =3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 y =5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 In the figure above, A BCD is a square. If 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 35. A certain cylindrical tank set on its A C is 8 units long, what is the perimeter 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 circular base is 7.5 feet in height. If the of the square? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tank is filled with water, and if the water 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 16 3456789012345678901234567890121234567890123456789012345678901212345 6 12 is then poured out of the tank into smaller 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 12 2 = 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 cube-shaped tanks, how many cube6 123456789012345678901234567890121234567890123456789012345678901212345 C. 24 6 123456789012345678901234567890121234567890123456789012345678901212345 shaped tanks are required to hold all the 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 16 =2 6 123456789012345678901234567890121234567890123456789012345678901212345 water? 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 30 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) The length of a cube-shaped tank’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 side is equal to the radius of the 6 123456789012345678901234567890121234567890123456789012345678901212345 33. Dan drove home from college at an 6 123456789012345678901234567890121234567890123456789012345678901212345 cylindrical tank’s circular base. 6 123456789012345678901234567890121234567890123456789012345678901212345 average rate of 60 miles per hour. O n his 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 trip back to college, his rate was 10 miles (2) If 3 cube-shaped tanks are stacked on 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 per hour slower and the trip took him one top of one another, the top of the third 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 hour longer than the drive home. H ow far cube stacked is the same distance 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 is Dan’s home from the college? above the ground as the top of the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 cylindrical tank. A. 65 miles 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 100 miles 6 123456789012345678901234567890121234567890123456789012345678901212345 36. The average of seven numbers is 84. Six of 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 200 miles 6 123456789012345678901234567890121234567890123456789012345678901212345 the numbers are: 86, 82, 90, 92, 80, and 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 280 miles 6 123456789012345678901234567890121234567890123456789012345678901212345 81. What is the seventh number? 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 300 miles 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 76 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 77 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. 79 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 81 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 85 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 478 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 37. A solution of 60 ounces of sugar and 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 water is 20% sugar. H ow much water 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 must be added to make a solution that is 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 5% sugar? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 20 ounces 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. 80 ounces 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 100 ounces 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 120 ounces 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 180 ounces 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 479

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 41 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Sentence Correction Questions: (T hese directions w ill appear on your 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Sentence Correction question. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 This question presents a sentence, all or part of which is underlined. Beneath the sentence 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 you will find five ways of phrasing the underlined part. The first of these repeats the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 original; the other four are different. If you think the original is best, choose the first 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer; otherwise choose one of the others. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 This question tests correctness and effectiveness of expression. In choosing your answer, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 follow the requirements of Standard Written English; that is, pay attention to grammar, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 choice of words, and sentence construction. Choose the answer that produces the most 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 effective sentence; this answer should be clear and exact, without awkwardness, ambigu3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ity, redundancy, or grammatical error. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Critical Reasoning Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Critical R easoning question.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 For this question, select the best of the answer choices given. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Reading Comprehension Questions: (T hese directions w ill appear on 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 your screen before your first group of R eading Com prehension questions.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The questions in this group are based on the content of a passage. After reading the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage, choose the best answer to each question. Answer all the questions following the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage on the basis of what is stated or im plied in the passage. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 480 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3. The media often hastens to chastise 1. H ealth professionals widely concur that, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 celebrities who have come into sudden beyond a certain amount of exercise each 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 and unexpected prominence, whether they day, the benefits that an individual can 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 expect to derive by further exercise is be actors, musicians, or some other 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 negligible. high-profile vocation. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 A. by further exercise is A. they be actors, musicians, or some 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. from further exercise are other high-profile vocation 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 C. in furthering exercise are B. their vocation be acting, music 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. by exercising further would be performance, or some other high3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. by exercising even more would be profile vocation 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. they be actors, music, or some other 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2. After bounty hunters turn over their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 high profile vocation 3456789012345678901234567890121234567890123456789012345678901212345 6 12 captives to the authorities, they often are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. their vocation is that of actor, 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 denied due process of law. 123456789012345678901234567890121234567890123456789012345678901212345 musician, or otherwise a high-profile 6 6 123456789012345678901234567890121234567890123456789012345678901212345 one 6 123456789012345678901234567890121234567890123456789012345678901212345 A. After bounty hunters turn over their 6 123456789012345678901234567890121234567890123456789012345678901212345 E. they are actors, are musicians, or in 6 123456789012345678901234567890121234567890123456789012345678901212345 captives to the authorities, they often 6 123456789012345678901234567890121234567890123456789012345678901212345 some other high-profile vocation 6 123456789012345678901234567890121234567890123456789012345678901212345 are denied due process of law. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. After turning over bounty hunters’ 6 123456789012345678901234567890121234567890123456789012345678901212345 4. In a recent survey, nine out of ten people 6 123456789012345678901234567890121234567890123456789012345678901212345 captives to the authorities, the 6 123456789012345678901234567890121234567890123456789012345678901212345 using Slim-Ease for two weeks as directed 6 123456789012345678901234567890121234567890123456789012345678901212345 authorities often deny them due 6 123456789012345678901234567890121234567890123456789012345678901212345 reported that they lost weight during this 6 123456789012345678901234567890121234567890123456789012345678901212345 process of law. 6 123456789012345678901234567890121234567890123456789012345678901212345 period. This fact surely proves that 6 123456789012345678901234567890121234567890123456789012345678901212345 C. The authorities often deny captives 123456789012345678901234567890121234567890123456789012345678901212345 Slim-Ease is effective for anyone wanting 6 6 123456789012345678901234567890121234567890123456789012345678901212345 due process of law after bounty 6 123456789012345678901234567890121234567890123456789012345678901212345 to shed some unwanted pounds. 6 hunters turn the captives over to the 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The claim made above depends on which 6 authorities. 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of the following assumptions? D. Bounty hunters turn over their 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 captives to the authorities, often being 6 123456789012345678901234567890121234567890123456789012345678901212345 A. The survey participants were not 6 123456789012345678901234567890121234567890123456789012345678901212345 denied due process of law. 6 123456789012345678901234567890121234567890123456789012345678901212345 using Slim-Ease immediately prior to 6 123456789012345678901234567890121234567890123456789012345678901212345 E. A captive, when turned over by 6 123456789012345678901234567890121234567890123456789012345678901212345 the two-week period. 6 123456789012345678901234567890121234567890123456789012345678901212345 bounty hunters to the authorities, is 6 123456789012345678901234567890121234567890123456789012345678901212345 B. The survey participants did not 6 123456789012345678901234567890121234567890123456789012345678901212345 often denied due process of law. 123456789012345678901234567890121234567890123456789012345678901212345 exercise during the two-week period. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. The survey participants were over123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 weight prior to the two-week period. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 D. The survey participants’ dietary habits 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 were otherwise similar during the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 two-week period as prior to that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 period. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. N o other product is more effective 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 than Slim-Ease to help lose weight. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 481

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 5. Compared to older houses, new houses assumed that, since European N ew 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (10) are sure to have newer, more efficient Towns had been financially and socially 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 heating and cooling units, more modern successful, the same could be expected in 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 kitchen appliances, and more contempothe United States. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rary-style bathroom fixtures. They also H owever, the ill-considered projects 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 generally conform to current buildingnot only failed to relieve pressures on 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (15) code regulations, whereas many older existing cities, but also weakened those 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 houses do not. Accordingly, it is always cities further by drawing away high6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 advantageous to purchase a new home income citizens. This increased the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rather than an old home. concentration of low-income groups— 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 who were unable to provide the neces6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if true, is the best 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (20) sary tax base to support the cities. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 criticism of the advice given in the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Taxpayers who remained were left to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 argument above? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 carry a greater burden, while industry 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Some people prefer more traditional 6 123456789012345678901234567890121234567890123456789012345678901212345 and commerce sought to escape. 6 123456789012345678901234567890121234567890123456789012345678901212345 styles of bathroom fixtures over 6 123456789012345678901234567890121234567890123456789012345678901212345 As it turned out, the promoters of 6 123456789012345678901234567890121234567890123456789012345678901212345 contemporary styles. 6 123456789012345678901234567890121234567890123456789012345678901212345 (25) N ew Towns were the developers, 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Whether a house has new equipment builders, and financial institutions, all 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and fixtures and conforms to current whose main interest was financial gain. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 code requirements are not the only N ot surprisingly, development occurred 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 factors home buyers consider imporin areas where land was cheap and 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 tant when choosing a house. (30) construction profitable rather than where 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. N ew houses are generally more N ew Towns were genuinely needed. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 expensive than older houses of M oreover, poor planning and legislation 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 comparable size. produced not the sort of successful N ew 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 D. When an older house is sold, correctTowns seen in Britain but rather nothing 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ing any code violations is the respon(35) more than sprawling suburbs. Federal 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 sibility of the seller. regulations designed to promote the N ew 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. In general, older houses have more of Town concept failed to consider social 6 123456789012345678901234567890121234567890123456789012345678901212345 the kinds of details that lend charm to 6 123456789012345678901234567890121234567890123456789012345678901212345 needs as the European plans did. In fact, 6 123456789012345678901234567890121234567890123456789012345678901212345 a home than do new houses. 6 123456789012345678901234567890121234567890123456789012345678901212345 the regulations specified virtually all of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (40) the ingredients of the typical suburban 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 community. Questions 6–8 are based on the following 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 passage: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Line In the 1970s, the idea of building 6 123456789012345678901234567890121234567890123456789012345678901212345 6 so-called “ N ew Towns” to absorb 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 growth was considered a potential 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 cure-all for urban problems in the United 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (5) States. It was erroneously assumed that 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 by diverting residents from existing 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 centers, current urban problems would at 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 least get no worse. It was also wrongly 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 482 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 8. Which of the following phenomena is 6. The author’s primary concern in the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most closely analogous to the N ew Towns 6 passage is to 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 established in the United States? 6 123456789012345678901234567890121234567890123456789012345678901212345 A. describe the characteristics of Ameri2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. A business that fails as a result of can N ew Towns that made them 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 insufficient demand for its products or 6 unsuccessful. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 services B. trace the development of the N ew 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. A new game that fails to attain Town concept in the United States. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 widespread popularity because its C. list the differences between N ew 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rules are unfair Towns in the United States with those 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. N ew utility software that solves one in Europe. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 computer problem but creates another 6 D. explain why N ew Towns in the United 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. A new drug whose side effects are Stated failed to meet general expecta3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 severe enough to discourage people tions. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 from using it E. analyze the impact of N ew Towns on 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. A scientific theory that lacks support- 6 urban centers in the United States. 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ing empirical evidence 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 7. Based only on the information in the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 9. The rules of etiquette for formal dinner passage, with which of the following 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 parties with foreign diplomats require statements about N ew Towns in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 citizens from both the host and from the United States would the author most 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 likely agree? diplomat’s countries to be seated across 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from each other. 6 123456789012345678901234567890121234567890123456789012345678901212345 A. They helped dissuade businesses in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 urban centers from relocating to other A. citizens from both the host and from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 areas. the diplomat’s countries to be seated 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. They provided a thriving social center across from each other 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 away from the problems of the older B. citizens of the host country and of the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 city. diplomat’s party to sit opposite each 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. They helped reduce air pollution by other 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 relocating workplaces to suburbs, C. that the host country and diplomat’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 where most workers lived. country seat their citizens opposite 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. They thwarted economic redevelopone another 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ment plans for decaying urban D. that citizens of the host country be 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 centers. seated opposite those of the diplo6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. They provided affluent urban mat’s country 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 residents an escape from the city. E. the host county’s citizens to be seated 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 opposite to the diplomat’s country’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 citizens 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 483

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 11. G w en: As we both know, the most 10. Com pany X spok esperson: Although 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 popular restaurants among college several of our key managerial employees 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 students here in Collegetown are the ones have left our company since we merged 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 that provide delivery service. So, local with our leading competitor two months 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 economic conditions, which rely on the ago, we have no reason to believe that a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 student population, would improve if significant number of our other employees 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 expensive Collegetown restaurants were will follow suit. Virtually all of Company 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 replaced by less expensive ones that also X’s current employees are the same people 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 provide delivery service. who we employed prior to the merger, and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 our employee-relations department is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Jose: I disagree. After all, many expensive 6 123456789012345678901234567890121234567890123456789012345678901212345 making every effort to ensure that these 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Collegetown restaurants also provide 3456789012345678901234567890121234567890123456789012345678901212345 6 12 employees are content here. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 delivery service. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would Which of the following best expresses the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tend to support most effectively the point of disagreement between Gwen 3456789012345678901234567890121234567890123456789012345678901212345 6 12 spokesperson’s prediction in the argument 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and Jose? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 above? 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. whether inexpensive restaurants are 6 123456789012345678901234567890121234567890123456789012345678901212345 A. The employees who left Company X 6 123456789012345678901234567890121234567890123456789012345678901212345 more popular among Collegetown 6 123456789012345678901234567890121234567890123456789012345678901212345 since the merger did so because they 6 123456789012345678901234567890121234567890123456789012345678901212345 students than expensive restaurants 6 123456789012345678901234567890121234567890123456789012345678901212345 received more attractive employment 6 123456789012345678901234567890121234567890123456789012345678901212345 B. whether Collegetown should reduce 6 123456789012345678901234567890121234567890123456789012345678901212345 offers from other firms. 6 123456789012345678901234567890121234567890123456789012345678901212345 the number of restaurants providing 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Worsening economic conditions may 6 123456789012345678901234567890121234567890123456789012345678901212345 delivery service 6 123456789012345678901234567890121234567890123456789012345678901212345 force Company X to reduce the size of 6 123456789012345678901234567890121234567890123456789012345678901212345 C. whether inexpensive restaurants in 6 123456789012345678901234567890121234567890123456789012345678901212345 its workforce in the near future. 123456789012345678901234567890121234567890123456789012345678901212345 Collegetown should provide delivery 6 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Company X has just hired a highly 6 123456789012345678901234567890121234567890123456789012345678901212345 service 6 123456789012345678901234567890121234567890123456789012345678901212345 respected consultant who specializes 123456789012345678901234567890121234567890123456789012345678901212345 D. whether Collegetown students prefer 6 6 123456789012345678901234567890121234567890123456789012345678901212345 in employee relations. delivery meal service over sit-down 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. N one of the employees who worked meal service 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for the company that has merged with E. whether inexpensive restaurants are 6 123456789012345678901234567890121234567890123456789012345678901212345 Company X have left voluntarily. 6 123456789012345678901234567890121234567890123456789012345678901212345 popular among Collegetown students 6 123456789012345678901234567890121234567890123456789012345678901212345 E. M ost companies lose some workers to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 other firms as a result of a merger, but 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the number of workers lost is usually 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 insignificant. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 484 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 14. If the corporate bureaucracy persists in its 6 12. Whether the universe is bound is fre123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 discriminatory hiring and job advancequently asked but impossible to answer. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 ment practices, its chief executives will 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Whether the universe is bound is 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 expose themselves to class-action litigation 6 3456789012345678901234567890121234567890123456789012345678901212345 12 frequently asked but impossible to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 by the groups prejudiced thereby. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. A question asked frequently is A. its chief executives will expose 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 whether the universe is bound, and it themselves 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 is impossible to answer. B. its chief executives would expose 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. As to whether the universe is bound is themselves 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 frequently asked but impossibly C. their chief executives will expose 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 answered question. themselves 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 D. Whether the universe is bound is D. its chief executives themselves would 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 frequently asked but impossible become exposed 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 answered. E. the chief executives will, by them6 123456789012345678901234567890121234567890123456789012345678901212345 E. Whether or not the universe is bound selves, be exposed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is a question asked frequently but a 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 question impossible to answer. 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 15–17 are based on the following 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage: 6 123456789012345678901234567890121234567890123456789012345678901212345 13. O f the 1,000 chemicals in coffee, less than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Line When Ralph Waldo Emerson prothirty have been tested, most of which 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 nounced America’s declaration of produce cancer in laboratory rats. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 cultural independence from Europe in his 6 6 123456789012345678901234567890121234567890123456789012345678901212345 A. less than thirty have been tested, most “ American Scholar” address, he was 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of which produce cancer in laboratory actually articulating the transcendental (5) 123456789012345678901234567890121234567890123456789012345678901212345 66 rats 123456789012345678901234567890121234567890123456789012345678901212345 assumptions of Jefferson’s political 6 123456789012345678901234567890121234567890123456789012345678901212345 B. most of which produce cancer in 6 123456789012345678901234567890121234567890123456789012345678901212345 independence. In the ideal new world 6 123456789012345678901234567890121234567890123456789012345678901212345 laboratory rats, fewer than thirty have 6 123456789012345678901234567890121234567890123456789012345678901212345 envisioned by Emerson, America’s 6 123456789012345678901234567890121234567890123456789012345678901212345 been tested 6 123456789012345678901234567890121234567890123456789012345678901212345 becoming a perfect democracy of free 6 123456789012345678901234567890121234567890123456789012345678901212345 C. most of the less than thirty tested 6 123456789012345678901234567890121234567890123456789012345678901212345 and self-reliant individuals was within (10) 6 123456789012345678901234567890121234567890123456789012345678901212345 produced cancer in laboratory rats 6 123456789012345678901234567890121234567890123456789012345678901212345 reach. Bringing Emerson’s metaphysics 6 123456789012345678901234567890121234567890123456789012345678901212345 D. less than thirty of which have been 6 123456789012345678901234567890121234567890123456789012345678901212345 down to earth, H enry David Thoreau’s 6 123456789012345678901234567890121234567890123456789012345678901212345 tested, most of them produce cancer 123456789012345678901234567890121234567890123456789012345678901212345 W alden (1854) asserted that one can live 6 6 123456789012345678901234567890121234567890123456789012345678901212345 in laboratory rats 6 123456789012345678901234567890121234567890123456789012345678901212345 without encumbrances. Emerson wanted 6 123456789012345678901234567890121234567890123456789012345678901212345 E. fewer than thirty have been tested, 6 123456789012345678901234567890121234567890123456789012345678901212345 to visualize Thoreau as the ideal scholar (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 and most of these produce cancer in 6 123456789012345678901234567890121234567890123456789012345678901212345 in action that he had called for in the 6 123456789012345678901234567890121234567890123456789012345678901212345 laboratory rats 123456789012345678901234567890121234567890123456789012345678901212345 “ American Scholar.” In the end, however, 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Emerson regretted Thoreau’s too-private 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 individualism, which failed to signal the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 vibrant revolution in national conscious- 6 (20) 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ness that Emerson had prophesied. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 For Emerson, what Thoreau lacked, Walt 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Whitman embodied in full. O n reading 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 L eaves of G rass (1855), Emerson saw in 6 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 485

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 16. Based on the passage’s information, it can 6 (25) Whitman the “ prophet of democracy” 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be inferred that Emerson might be whom he had sought. O ther American 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 characterized as any of the following Renaissance writers were less optimistic 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 EXCEPT than Emerson and Whitman about the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 fulfillment of the democratic ideal. In 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. a transcendentalist. 6 123456789012345678901234567890121234567890123456789012345678901212345 T he Scarlet L etter (1850), N athaniel (30) 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. an American Renaissance writer. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 H awthorne concluded that antinomian3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. a public speaker. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ism such as the “ heroics” displayed by 6 123456789012345678901234567890121234567890123456789012345678901212345 D. a would-be prophet. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 H ester Prynne leads to moral anarchy; 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. a political pragmatist. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and H erman M elville, who saw in his 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 story of Pierre (1852) a metaphor for the (35) 17. With which of the following statements 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 misguided assumptions of democratic about M elville and H awthorne would the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 idealism, declared the transcendentalist author most likely agree? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 dream unrealizable. Ironically, the 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Both men were disillusioned transcen6 123456789012345678901234567890121234567890123456789012345678901212345 literary vigor with which both H aw6 123456789012345678901234567890121234567890123456789012345678901212345 dentalists. 6 123456789012345678901234567890121234567890123456789012345678901212345 thorne and M elville explored the ideal (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. H awthorne sympathized with the 6 123456789012345678901234567890121234567890123456789012345678901212345 showed their deep sympathy with it even 6 123456789012345678901234567890121234567890123456789012345678901212345 transcendental dream more so than as they dramatized its delusions. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 M elville. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. They agreed as to what the transcen- 6 123456789012345678901234567890121234567890123456789012345678901212345 15. The author of the passage seeks prima123456789012345678901234567890121234567890123456789012345678901212345 dentalist dream would ultimately lead 6 6 123456789012345678901234567890121234567890123456789012345678901212345 rily to 6 123456789012345678901234567890121234567890123456789012345678901212345 to. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Both men believed the idealists to be A. explore the impact of the American 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 misguided. Renaissance writers on the literature 6 123456789012345678901234567890121234567890123456789012345678901212345 E. H awthorne politicized the transcen6 of the late 18th Century. 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 dental ideal, whereas M elville B. illustrate how American literature of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 personalized it. the mid-18th century differed in form 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 from European literature of the same 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 time period. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. identify two schools of thought 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 among American Renaissance writers 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 regarding the democratic ideal. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. point out how Emerson’s democratic 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 idealism was mirrored by the works 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of the American Renaissance writers. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. explain why the writers of the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 American Renaissance believed that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 an ideal world was forming in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 America. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 486 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 19. Analyst Q predicts that the share price of 6 18. Last year, two drownings occurred at Lake 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M etaCorp stock will remain at its current 6 Serene, so this year the lake’s owner added 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 level or higher as long as most stock one more lifeguard to the lakefront staff. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 analysts continue to recommend that N o drownings have occurred at the lake 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 investors buy the company’s stock, and this year. H owever, the new lifeguard has 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 that stock analysts will continue to been home with the flu for nearly half the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 recommend M etaCorp stock to investors summer, so it appears that the new 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 as long as the company continues to show 6 lifeguard was not needed after all. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 a profit. Analyst T predicts that the share 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would be 3456789012345678901234567890121234567890123456789012345678901212345 6 12 price of M etaCorp stock will at least 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most damaging to the argument above? 6 123456789012345678901234567890121234567890123456789012345678901212345 remain at its current level, even if eco2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. This year, the lake’s owner posted a nomic conditions worsen for M etaCorp’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 warning about swimming without a 3456789012345678901234567890121234567890123456789012345678901212345 12 industry as a whole, as long as M etaCorp 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 lifeguard present. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 continues to show a profit. 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Drowning is not the lake owner’s only 6 123456789012345678901234567890121234567890123456789012345678901212345 If the predictions of Analyst Q and 6 123456789012345678901234567890121234567890123456789012345678901212345 safety concern. 6 123456789012345678901234567890121234567890123456789012345678901212345 Analyst T are all accurate, which of the 6 123456789012345678901234567890121234567890123456789012345678901212345 C. The lake has been equally crowded 6 123456789012345678901234567890121234567890123456789012345678901212345 following is logically inferable from them? 6 123456789012345678901234567890121234567890123456789012345678901212345 with swimmers this year as last year. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. Stock analysts would be more likely D. Lake activities are safer in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to recommend M etaCorp stock to presence of lifeguards. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 investors if economic conditions for E. The new lifeguard has never saved a 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 M etaCorp’s industry are good than if 6 person from drowning. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 they are poor. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. If M etaCorp discontinues to show a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 profit, stock analysts will be less 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 inclined to recommend the company’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 stock to investors. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. If stock analysts stop recommending 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 M etaCorp stock to investors, then the 6 123456789012345678901234567890121234567890123456789012345678901212345 price of M etaCorp stock is less likely 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to at least remain at its current level 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 than if stock analysts continue to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 recommend it. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. If economic conditions worsen for 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 M etaCorp’s industry as a whole, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 stock analysts will be less inclined to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 recommend M etaCorp stock. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. If M etaCorp continues to show a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 profit, then the price of M etaCorp 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 stock will either remain at its current 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 level or increase. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 487

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 21. The high level of violence in television 20. A national performing arts association 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 programming today has often been cited conducted a survey that appears to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 as an explanation for the increasing level confirm the public’s interest in high 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 of violence in our society. And, in fact, culture. M ore than ninety percent of those 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 some recent studies show that the level of surveyed said that they were either 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 violence in television programming has “ somewhat interested” or “ very inter6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 increased considerably over the past ested” in attending performances of opera, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 twenty years. H owever, other recent ballet, or classical music. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 studies indicate that the level, while high, 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would 3456789012345678901234567890121234567890123456789012345678901212345 6 12 is only slightly greater than it was twenty 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most seriously weaken the argument 6 123456789012345678901234567890121234567890123456789012345678901212345 years ago. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 above? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would A. N ot all performances of opera, ballet, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 provide the best explanation for the and classical music should be consid2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 discrepancy among the recent studies cited ered “ high culture.” 6 123456789012345678901234567890121234567890123456789012345678901212345 in the argument above? 6 123456789012345678901234567890121234567890123456789012345678901212345 B. N ot all those who are interested in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. N umerous studies of television attending performances of opera, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 violence have been conducted since ballet, or classical music are willing to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the advent of television, and their support an arts association. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 results have not always been in C. M ost of those surveyed reported being 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 agreement. “ somewhat interested” rather than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. All of those involved in conducting “ highly interested.” 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the cited studies shared the same D. O ther statistics show that more 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 perception of what constitutes people attend sporting events than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 “ violence” in television programming. performances of opera, ballet, or 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. Television programming designed classical music. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 specifically for children accounts for a 6 E. The association conducting the survey 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 greater portion of television program- 6 receives most of its funding from 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ming today than it did twenty years sources other than the general public. 6 123456789012345678901234567890121234567890123456789012345678901212345 ago. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. M any factors other than violence in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 television programming carry a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 significant impact on the level of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 violence in society. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. O ver the last twenty years, the level of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 violence in television programming 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 has increased more than in society as 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 a whole. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 488 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 25. In general, obesity is caused not by the 22. All modern computer languages derive 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ingestion of foods that are high in fat from a more basic “ assembly” language 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 content but rather by eating foods that that originated many decades ago. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 contain too much sugar. For proof, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. All modern computer languages 3456789012345678901234567890121234567890123456789012345678901212345 6 12 consider that over the past ten years, even 3456789012345678901234567890121234567890123456789012345678901212345 6 12 derive from 6 123456789012345678901234567890121234567890123456789012345678901212345 as sales of low-fat meals, snacks, and 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. Derived from all modern computer 3456789012345678901234567890121234567890123456789012345678901212345 6 12 desserts have increased sharply through3456789012345678901234567890121234567890123456789012345678901212345 6 12 languages is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 out the world’s developed countries, the 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Resulting in all modern computer 2 3456789012345678901234567890121234567890123456789012345678901212345 1 incidence of obesity in those countries, as 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 languages was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a percentage of overall population, has 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. M odern computer languages, which 6 123456789012345678901234567890121234567890123456789012345678901212345 reached a new high. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 all resulted from 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would E. All modern computer languages are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most support the claim made in the derived from 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 argument above? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 23. Despite his admiration of the great jazz 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. N inety percent of the low-fat foods 3456789012345678901234567890121234567890123456789012345678901212345 6 12 musicians that preceded him, Blakey 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 sold in developed countries are 6 123456789012345678901234567890121234567890123456789012345678901212345 opposed them trivializing the popular 6 123456789012345678901234567890121234567890123456789012345678901212345 purchased by just ten percent of the 6 123456789012345678901234567890121234567890123456789012345678901212345 genre. 6 123456789012345678901234567890121234567890123456789012345678901212345 population. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. them trivializing the popular genre B. Sales of foods with a high sugar 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. their trivializing of the popular genre content have increased significantly 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. them when trivializing the popular over the past ten years. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 genre C. Government-approved standards of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. the popular genre being trivialized by obesity have changed several times 6 123456789012345678901234567890121234567890123456789012345678901212345 6 them 123456789012345678901234567890121234567890123456789012345678901212345 during the past ten years. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. their trivializing the popular genre 123456789012345678901234567890121234567890123456789012345678901212345 D. Some foods labeled “ low-fat” actually 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 contain relatively high levels of fat. 6 123456789012345678901234567890121234567890123456789012345678901212345 24. Inventors have yet to learn that something 6 123456789012345678901234567890121234567890123456789012345678901212345 E. M ost physicians consider regular 6 123456789012345678901234567890121234567890123456789012345678901212345 that does two things does one of them 6 123456789012345678901234567890121234567890123456789012345678901212345 exercise to be an important compo6 123456789012345678901234567890121234567890123456789012345678901212345 better. nent of any effective program to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prevent or reverse obesity. 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Inventors have yet to learn 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. H aving not yet learned, inventors 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 need to learn 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. Inventors have not as of yet learned 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Inventors as yet have to learn 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. N ot having yet learned, inventors 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 have to learn 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 489

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 28–30 are based on the following 26. The increasing scarcity of available rental 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 passage: housing, particularly apartments with two 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 or more bedrooms, is attributable to two 6 123456789012345678901234567890121234567890123456789012345678901212345 Line During the process of embryonic 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 recent trends: the increasing number of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 development, cells become progressively 3456789012345678901234567890121234567890123456789012345678901212345 6 12 new office buildings as compared to new 3456789012345678901234567890121234567890123456789012345678901212345 6 12 restricted in their developmental poten6 123456789012345678901234567890121234567890123456789012345678901212345 apartment buildings and the increasing 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 tial and finally acquire the biochemical 3456789012345678901234567890121234567890123456789012345678901212345 6 12 number of rental apartments being sold as 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and morphological specialization (5) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 condominiums rather than rented. 6 123456789012345678901234567890121234567890123456789012345678901212345 necessary for their respective functions in 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The passage above best supports which of an adult. Since enzymatic and structural 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 the following conclusions? proteins are required for the appearance 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 and maintenance of this specialization, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. The rate at which new apartment 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the differentiated state results from the (10) buildings are being built is decreasing. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 synthesis and activity of cell-specific B. The current demand for reasonably 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 proteins during development. priced rental housing is greater than 6 123456789012345678901234567890121234567890123456789012345678901212345 Since all cells of an organism contain 6 123456789012345678901234567890121234567890123456789012345678901212345 the current supply. 6 123456789012345678901234567890121234567890123456789012345678901212345 the same genotype as the fertilized egg, 6 123456789012345678901234567890121234567890123456789012345678901212345 C. M ost rental apartments being sold as 6 123456789012345678901234567890121234567890123456789012345678901212345 cellular differentiation is the result of (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 condominiums have at least two 6 123456789012345678901234567890121234567890123456789012345678901212345 variable gene activity rather than 6 123456789012345678901234567890121234567890123456789012345678901212345 bedrooms. 6 123456789012345678901234567890121234567890123456789012345678901212345 selective gene loss. Thus, cellular 6 123456789012345678901234567890121234567890123456789012345678901212345 D. M ore new office buildings than rental 6 123456789012345678901234567890121234567890123456789012345678901212345 specialization and cell-specific protein 6 123456789012345678901234567890121234567890123456789012345678901212345 apartment buildings are currently 6 123456789012345678901234567890121234567890123456789012345678901212345 synthesis result from the expression of 6 123456789012345678901234567890121234567890123456789012345678901212345 being built. 6 123456789012345678901234567890121234567890123456789012345678901212345 appropriately selected groups of genes in (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 E. The current demand for offices is 6 123456789012345678901234567890121234567890123456789012345678901212345 each cell type. As development proceeds, 6 123456789012345678901234567890121234567890123456789012345678901212345 greater than the current demand for 6 123456789012345678901234567890121234567890123456789012345678901212345 the progressive differentiation of cells is 6 123456789012345678901234567890121234567890123456789012345678901212345 rental apartments. 6 123456789012345678901234567890121234567890123456789012345678901212345 correlated with changes in the population 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of protein species within the embryo, 27. Scientist and artist Leonardo Da Vinci 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 which in turn reflect the accurate (25) was, and always will be considered by 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 programming of the time and sequence of 6 many, as a singular figure among those 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the biosynthesis of different proteins by whose scientific, artistic, and other 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the genome. In the absence of opportuni- 6 cultural contributions defined the Renais123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ties for genetic analysis, determining the sance period of European history. 6 123456789012345678901234567890121234567890123456789012345678901212345 mechanisms involved in the regulation of 6 (30) 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. was, and always will be considered by protein synthesis is key to understanding 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 many, as genome control during development. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. was and always will be considered by The majority of studies on gene 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 many as being activity in embryogenesis have been done 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. was, and always will be by many, on the sea urchin system, where large (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 considered numbers of embryos undergoing rela6 123456789012345678901234567890121234567890123456789012345678901212345 D. was, and always will be considered by 6 123456789012345678901234567890121234567890123456789012345678901212345 tively synchronous development can be 6 123456789012345678901234567890121234567890123456789012345678901212345 many as, 6 123456789012345678901234567890121234567890123456789012345678901212345 easily obtained. Also, sea urchins’ 6 123456789012345678901234567890121234567890123456789012345678901212345 E. was considered by many and always 6 123456789012345678901234567890121234567890123456789012345678901212345 permeability to radioactive isotopes and 6 123456789012345678901234567890121234567890123456789012345678901212345 will be by many 6 123456789012345678901234567890121234567890123456789012345678901212345 to inhibitors of RN A and protein (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 490 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 29. Which of the following statements about synthesis provides a distinct advantage 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 embryonic development in sea urchins is for study over amphibian material. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 best supported by the passage? Especially well documented are the 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 maternal programming of early develop3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Genomic control over early embry3456789012345678901234567890121234567890123456789012345678901212345 6 12 ment and the genomic control of later (45) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 onic development is especially well 6 123456789012345678901234567890121234567890123456789012345678901212345 differentiation in the urchin. M aternal 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 documented. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 products, stored in the egg cytoplasm 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. Permeability to RN A inhibitors is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 from oogenesis, can support development 6 123456789012345678901234567890121234567890123456789012345678901212345 comparable to that in amphibian 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 from fertilization through the hatching 3456789012345678901234567890121234567890123456789012345678901212345 6 12 embryos. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 blastula stage; however, development (50) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. Development during the hatching 6 123456789012345678901234567890121234567890123456789012345678901212345 from the mesenchyme blastula stage is 2 3456789012345678901234567890121234567890123456789012345678901212345 1 blastula stage requires gene products 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 dependent upon gene products synthe3456789012345678901234567890121234567890123456789012345678901212345 12 synthesized under the direction of the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 sized under the direction of the embry3456789012345678901234567890121234567890123456789012345678901212345 6 12 embryonic genome. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 onic genome. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. M aternal products can support 6 123456789012345678901234567890121234567890123456789012345678901212345 embryonic development following the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 28. With which of the following statements mesenchyme blastula stage. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 would the author of the passage most E. Genomic control of later cell differen- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 likely disagree? tiation has been studied extensively. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. M orphological specialization requires 6 123456789012345678901234567890121234567890123456789012345678901212345 30. The last paragraph of the passage 6 123456789012345678901234567890121234567890123456789012345678901212345 the synthesis of cell-specific proteins. 6 123456789012345678901234567890121234567890123456789012345678901212345 (lines 33–54) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Embryonic development involves 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 A. illustrates a biological process by way 6 differentiation in cell genotype. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of an example. C. The population of protein species 6 123456789012345678901234567890121234567890123456789012345678901212345 B. describes a methodology for studying 6 with the embryo is dependent upon 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a biological phenomenon. the timing of protein biosynthesis. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. compares two stages of biological D. Enzymatic proteins are required for 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 development. an organism’s full development. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. defines and explains an important E. Selective gene loss is not a factor in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 term mentioned earlier. cellular differentiation during 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. provides an example which disproves embryonic development. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 a scientific theory. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 491

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 32. Due to sharply escalating tuition at 31. Equipment used by private biotechnology6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 four-year colleges, debt on student loans research firms becomes obsolete more 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 has increased to the point that many new quickly than any other business equip123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 graduates are forced either to pursue ment, simply because biotechnology 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 graduate-level degrees, thereby postponing advances so rapidly. A proposed tax law 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 repayment of their student loans, or to would provide significant tax incentives 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pursue only the highest-paying jobs. An for businesses in every industry to replace 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 unfortunate result of this trend is that their old equipment with new equipment. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 fewer and fewer new graduates are O bviously, political lobbyists for the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 entering important, but lower-paying, biotechnology industry were the instiga3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 professions that require only a four-year tors of this tax proposal. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 degree. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following most supports the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following strategies would claim that biotechnology industry lobby3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 be most effective in reversing the decline in 6 ists are responsible for the tax proposal? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the number of college graduates entering 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Equipment used in the biotechnology 3456789012345678901234567890121234567890123456789012345678901212345 6 12 lower-paying professions that require only 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 industry loses its value more quickly 6 123456789012345678901234567890121234567890123456789012345678901212345 a four-year degree? 6 123456789012345678901234567890121234567890123456789012345678901212345 than equipment used in any other 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. Encourage college students to enroll industry. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in classes year-round in order to B. Biotechnology firms expect biotech123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 graduate early. nology advances to outpace those in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Expand opportunities for graduateother industries for the foreseeable 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 level students to obtain paying jobs future. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 while still in school. C. The legislator introducing the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Expand course offerings that prepare proposed law used to work in the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 college students for these lowerbiotechnology industry. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 paying professions. D. O ther industries have not lobbied for 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 D. Establish higher admission standards 6 the proposed law. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 for graduate-level programs. E. Unless a biotechnology firm replaces 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Increase the number of academic units 6 its obsolete equipment, it will be 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 required to obtain a four-year college 6 driven out of business by competing 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 degree. firms. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 492 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 33. International environmental regulations 35. In order for a new third-world democratic 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 do not protect hybrid species, but they are country to achieve and maintain political 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 protected by way of domestic laws. stability, its government must afford its 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 citizens the power to elect and remove the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 A. but they are protected by way of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 country’s leaders. After all, Country X is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 domestic laws 6 123456789012345678901234567890121234567890123456789012345678901212345 among the most stable countries in the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. although domestic laws do 3456789012345678901234567890121234567890123456789012345678901212345 6 12 world, and its government affords its 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. and so domestic laws only protect 3456789012345678901234567890121234567890123456789012345678901212345 6 12 citizens this power. 6 123456789012345678901234567890121234567890123456789012345678901212345 hybrid species 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. yet the laws of domestic protection 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The argument above is flawed in that it 3456789012345678901234567890121234567890123456789012345678901212345 6 12 will so protect 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ignores the possibility that 6 123456789012345678901234567890121234567890123456789012345678901212345 E. which require legal protection 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. many third-world countries already domestically 3456789012345678901234567890121234567890123456789012345678901212345 6 12 grant their citizens the power to elect 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 34. Even for high school freshmen and and remove their leaders. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 sophomores, theories concerning the B. a large percentage of third-world 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 psychology of death and dying among the countries have already achieved, and 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 elderly can hold considerable significance are maintaining, political stability. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and interest for many students. C. Country X’s leaders are more popular 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 among Country X’s citizens than are 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Even for high school freshmen and 6 123456789012345678901234567890121234567890123456789012345678901212345 the leaders of most third-world 6 123456789012345678901234567890121234567890123456789012345678901212345 sophomores, theories concerning the psy6 123456789012345678901234567890121234567890123456789012345678901212345 countries among their citizens. 6 chology of death and dying among the 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. specific procedures for electing a elderly can hold considerable signifi6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 country’s leaders vary significantly cance and interest for many students. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 from one country to another. B. Even for high school freshmen and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Country X was already politically sophomore students with considerable 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 stable when its citizens were first interest in theories concerning the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 afforded the power to elect and psychology of death and dying among 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the elderly, these theories can hold remove their leaders. 6 123456789012345678901234567890121234567890123456789012345678901212345 considerable significance. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Theories concerning the psychology of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 death and dying among the elderly, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 for many students, even high school 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 freshmen and sophomores, can hold 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 considerable significance and interest. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Theories concerning the psychology of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 death and dying among the elderly 6 123456789012345678901234567890121234567890123456789012345678901212345 can hold considerable significance and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 interest even for high school freshmen 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and sophomore students. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. Considerable significance and interest 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for even high school freshmen and 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 sophomores is held in theories 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 concerning the psychology of death 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 and dying among the elderly. 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 493

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 contrast, the notation in the music of Questions 36–39 are based on the following 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 H aydn and M ozart from the second half 6 passage: 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 of the eighteenth century was more 6 123456789012345678901234567890121234567890123456789012345678901212345 Line The origin of the attempt to distinguish 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 complete than in the earlier styles, and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 early from modern music and to establish 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the instruments seemed familiar, so no (45) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the canons of performance practice for 6 123456789012345678901234567890121234567890123456789012345678901212345 “ special” knowledge appeared necessary. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 each lies in the eighteenth century. In the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Also, the music of H aydn and M ozart, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 first half of that century, when Telemann (5) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 having never ceased to be performed, had 6 123456789012345678901234567890121234567890123456789012345678901212345 and Bach ran the collegium musicum in 2 3456789012345678901234567890121234567890123456789012345678901212345 1 maintained some kind of oral tradition of 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Leipzig, Germany, they performed their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 performance practice. (50) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 own and other modern music. In the 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 German universities of the early twenti3456789012345678901234567890121234567890123456789012345678901212345 6 12 36. It can be inferred that the “ standard 3456789012345678901234567890121234567890123456789012345678901212345 6 12 eth century, however, the reconstituted (10) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 repertory” mentioned in lines 13–14 3456789012345678901234567890121234567890123456789012345678901212345 6 12 collegium musicum devoted itself to 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 might have included music 6 123456789012345678901234567890121234567890123456789012345678901212345 performing music from the centuries 6 123456789012345678901234567890121234567890123456789012345678901212345 before the beginning of the “ standard 6 123456789012345678901234567890121234567890123456789012345678901212345 A. that called for the use of obsolete 6 123456789012345678901234567890121234567890123456789012345678901212345 repertory,” by which was understood 6 123456789012345678901234567890121234567890123456789012345678901212345 instruments. 6 123456789012345678901234567890121234567890123456789012345678901212345 music from before the time of Bach and (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. of the early twentieth century. 6 123456789012345678901234567890121234567890123456789012345678901212345 H andel. 6 123456789012345678901234567890121234567890123456789012345678901212345 C. written by the performance-practice 6 123456789012345678901234567890121234567890123456789012345678901212345 Alongside this modern collegium 6 123456789012345678901234567890121234567890123456789012345678901212345 composers. 6 123456789012345678901234567890121234567890123456789012345678901212345 musicum, German musicologists devel6 123456789012345678901234567890121234567890123456789012345678901212345 D. written before the time of H andel. 6 123456789012345678901234567890121234567890123456789012345678901212345 oped the historical subdiscipline known 6 123456789012345678901234567890121234567890123456789012345678901212345 E. composed before 1700. 6 123456789012345678901234567890121234567890123456789012345678901212345 as “ performance practice,” which (20) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 included the deciphering of obsolete 37. According to the passage, performance 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 musical notation and its transcription practice in the early twentieth century 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 into modern notation, the study of involved all of the following EXCEPT 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 obsolete instruments, and—most 123456789012345678901234567890121234567890123456789012345678901212345 A. deciphering outdated music notation. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 importantly because all musical notation (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. studying instruments no longer in 6 123456789012345678901234567890121234567890123456789012345678901212345 is incomplete—the re-establishment of 6 123456789012345678901234567890121234567890123456789012345678901212345 common use. 6 123456789012345678901234567890121234567890123456789012345678901212345 lost oral traditions associated with those 6 123456789012345678901234567890121234567890123456789012345678901212345 C. reestablishing unannotated perform6 123456789012345678901234567890121234567890123456789012345678901212345 forgotten repertories. The cutoff date for 6 123456789012345678901234567890121234567890123456789012345678901212345 ing traditions. 6 123456789012345678901234567890121234567890123456789012345678901212345 this study was understood to be around 123456789012345678901234567890121234567890123456789012345678901212345 D. determining which musical instrument 6 1750, the year of Bach’s death. The (30) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to use. reason for this demarcation was that the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 E. transcribing older music into modern 6 music of Bach, H andel, Telemann, and 6 123456789012345678901234567890121234567890123456789012345678901212345 notation. 6 123456789012345678901234567890121234567890123456789012345678901212345 their contemporaries did call for obsolete 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 instruments and voices and unannotated 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 performing traditions. Furthermore, with (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a few exceptions, late baroque music had 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ceased to be performed for nearly a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 century, with the result that orally 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 transmitted performing traditions 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 associated with it were forgotten. In (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 494 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 1 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 40. Veterinarians have developed a new cat 38. According to the passage, German 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 food that contains medication to prevent musicologists of the early twentieth 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 hair balls from accumulating in a cat’s century limited performance practice to 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 stomach and digestive tract. H air balls are 6 pre-1750 works because 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 generally not harmful to cats, but they do 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. special knowledge was generally not 6 123456789012345678901234567890121234567890123456789012345678901212345 cause discomfort. Although the medicated 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 required to decipher pre-1750 music. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 food is effective, many cats develop an 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. unannotated performing traditions 3456789012345678901234567890121234567890123456789012345678901212345 6 12 allergic reaction to it that, left untreated, 6 123456789012345678901234567890121234567890123456789012345678901212345 had been maintained for later works. 2 3456789012345678901234567890121234567890123456789012345678901212345 1 can result in a harmful infection. Accord- 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. generally speaking, only music written 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ingly, those concerned about the health of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 before 1750 had ceased to be per6 123456789012345678901234567890121234567890123456789012345678901212345 their cats should not feed this food to 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 formed. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 them. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. the annotation for earlier works was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The answer to which of the following generally less complete than for the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 questions would be most useful to cat works of Bach and H andel. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 owners considering whether to feed the E. music written prior to 1750 was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 medicated food to their cats? considered obsolete. 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. H ow much of the medicated food 6 123456789012345678901234567890121234567890123456789012345678901212345 39. The author refers to modern performance 6 123456789012345678901234567890121234567890123456789012345678901212345 must a cat eat in order to develop an 6 123456789012345678901234567890121234567890123456789012345678901212345 practice as a “ subdiscipline” (line 19) 6 123456789012345678901234567890121234567890123456789012345678901212345 allergic reaction? 6 123456789012345678901234567890121234567890123456789012345678901212345 probably because it 6 123456789012345678901234567890121234567890123456789012345678901212345 B. H ow noticeable to humans are the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. was not sanctioned by the mainallergic reactions associated with 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 stream. ingesting the medicated food? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. required more discipline than perC. Are there effective methods of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 forming the standard repertory. 123456789012345678901234567890121234567890123456789012345678901212345 preventing hairballs other than 6 123456789012345678901234567890121234567890123456789012345678901212345 C. focused on particular aspects of the 6 123456789012345678901234567890121234567890123456789012345678901212345 feeding a cat the medicated food? 6 123456789012345678901234567890121234567890123456789012345678901212345 music being performed at the German 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Do cats typically develop similar 6 123456789012345678901234567890121234567890123456789012345678901212345 universities. 6 123456789012345678901234567890121234567890123456789012345678901212345 allergic reactions to other types of 6 123456789012345678901234567890121234567890123456789012345678901212345 D. involved deciphering obsolete musical 6 123456789012345678901234567890121234567890123456789012345678901212345 food as well? 6 123456789012345678901234567890121234567890123456789012345678901212345 notation. E. What percentage of all cat owners feed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. involved performing the works the medicated food to their pet cats? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that were being transcribed at the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 universities. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 495

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 41. O n this issue, this state’s elected officials 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ignored the wishes of their electorate, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 which cannot reasonably be disputed in 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 light of the legislative record. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. O n this issue, this state’s elected 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 officials ignored the wishes of their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 electorate, which 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 B. This state’s elected officials, ignoring 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 on this issue the wishes of their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 electorate, 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. That this state’s elected officials 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ignored the wishes of their electorate 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. O n this issue, the wishes of the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 electorate were ignored by this state’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 elected officials, and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. That the wishes of the electorate on 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 this issue were ignored by this state’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 elected officials 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 496 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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Answers and Explanations See Appendix for score conversion tables to determine your score. Be sure to keep a tally of correct and incorrect answers for each test section.

1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Issue—Evaluation and Scoring 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Evaluate your Issue-Analysis essay on a scale of 1 to 6 (6 being the highest score) according to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the following five criteria: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 1. Does your essay develop a position on the issue through the use of incisive reasons and 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 persuasive examples? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Are your essay’s ideas conveyed clearly and articulately? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay maintain proper focus on the issue, and is it well organized? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure, vocabulary, and idiom? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument—Evaluation and Scoring 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Evaluate your Argument-Analysis essay on a scale of 1 to 6 (6 being the highest score) according 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to the following five criteria: 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. Does your essay identify the key features of the argument and analyze each one in a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 thoughtful manner? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Does your essay support each point of its critique with insightful reasons and examples? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay develop its ideas in a clear, organized manner, with appropriate 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 transitions to help connect ideas? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure, vocabulary, and idiom? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The following series of questions, which serve to identify the Argument’s five distinct problems, 6 123456789012345678901234567890121234567890123456789012345678901212345 will help you evaluate your essay in terms of criteria 1 and 2. To earn a score of 4 or higher, your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 essay should identify at least three of these problems and, for each one, provide at least one 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 497

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 example or counterexample that supports your critique. (Your examples need not be the same 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 as the ones below.) Identifying and discussing at least four of the problems would help earn you 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 an even higher score. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 • Do M axtech employees, at least those who claim Workforce cites, constitute a suffi3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 ciently representative statistical sam ple of the entire private-sector workforce? (Perhaps 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 these M axtech employees were more receptive or responsive to Workforce’s particular 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 methods than the average private-sector worker.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 • Is the report from Workforce Systems credible? (Perhaps the company overstates the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 benefits of its seminars in order to attract clients.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 • Was the seminar the actual cause of the improved level of contentment among the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 participants from M axtech? (The answer might depend on how much time has passed 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 since the seminar, whether M axtech’s participants have the same jobs as before, and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 whether the seminar is designed to help workers become more content to begin with.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 • Are the claims by M axtech’s employees credible? (Perhaps they felt pressure to exagger- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ate the benefits of the seminar, or falsely report improvement in order to take time off 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from work to enroll again in the seminar.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 • M ight the argument assume that all other conditions rem ain unchanged? (O verall 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 productivity of the economy’s private sector depends also on many extrinsic factors 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 having nothing to do with the benefits of these types of seminars.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Quantitative Ability 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. C Your first step is to rewrite mixed numbers as fractions: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 9 15 12 6 123456789012345678901234567890121234567890123456789012345678901212345 1 2 . 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 4 5 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The least common denominator is 20. You can eliminate answer choice (D). Rewrite 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 each fraction, then combine: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 9 15 12 90 1 75 2 48 117 6 123456789012345678901234567890121234567890123456789012345678901212345 1 2 5 5 6 123456789012345678901234567890121234567890123456789012345678901212345 2 4 5 20 20 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2. B You can solve the problem algebraically as follows: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 23 2 x 5 2~15 2 x ! 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 23 2 x 5 30 2 2x 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 57 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 An alternative method is to subtract the number given in each answer choice, in turn, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from both Lyle’s age and M elanie’s age. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 498 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3. C N either statement (1) nor (2) alone provides any information about the second variable 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 or, in turn, about the value of x 1 y 2 1. Thus (A), (B), and (D) can easily be eliminated. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 N ext, consider statements (1) and (2) together. Given a remainder of 2 when x is divided 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 by 3, the value of x must be greater than a multiple of 3 by exactly 2: x 5{5,8,11,14, . . .}. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Given a remainder of 5 when y is divided by 6, the value of y must be greater than a 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 multiple of 6 by exactly 5: y 5 {11,17,23,29, . . .}. Adding together any x -value and any 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 y-value will always result in a sum that exceeds a multiple of 3 by exactly 7 (or by exactly 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 1). Accordingly, subtracting 1 from that sum will always result in a multiple of 3. Thus, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 given statements (1) and (2), x 5 y 2 1 is divisible by 3. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 4. D Statement (1) alone suffices to answer the question. Given A C , BD , A B (which is 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 less than A C) must be less than BD . BD . A B, and the answer to the question is no. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A D 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Statement (2) also suffices alone to answer the question. Given 5 5 CD , C 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 bisects A D , and A C 5 CD . Thus, A B (which is smaller than A C) must be smaller than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 CD . Because CD is less than BD , A B , BD , and the answer to the question is no. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. C N either statement (1) nor (2) alone suffices to determine the values of both x and y. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Thus, you can easily eliminate choices (A), (B), and (D). N ext, consider both 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 statements together. The two-digit prime numbers less than 23 include 11, 13, 17, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and 19. Their sum is 60, and the average of the four numbers is 15. (x 5 15.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Considering statement (2), the positive factors of 60 that are less than 6 include 1, 2, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 3, 4, and 5. Their sum is 15 (y 5 15). x 5 y, and the answer to the question, based on 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 statements (1) and (2) together, is no. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6. E Statement (1) alone provides no information about how long it took David to travel 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the first 15 miles, and is therefore insufficient by itself to answer the question. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) alone provides even less information about how long it took David to 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 travel the entire distance. Although you can determine from statement (2) that David 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 traveled the first 17 miles in 45 minutes, you cannot determine how long it took 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 David to travel the remaining 13 miles. Statements (1) and (2) together establish that 6 123456789012345678901234567890121234567890123456789012345678901212345 David traveled 32 miles (17 1 15) in 85 minutes (45 1 40). H owever, 2 of the 32 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 miles are accounted for twice. Without knowing either the time that it took David to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 travel the 16th and 17th miles of the race, or his average speed over those two miles, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 you cannot determine David’s total time for the 30-mile race. Thus, statements (1) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and (2) together are insufficient to answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 7. A This question involves two steps. First, visually compare the difference in height 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 between Country X’s solid bar and shaded bar for each year. (Be careful to look at 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 County X’s bar, not Country Y’s.) You don’t need too determine amounts at this 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 point. A quick inspection reveals that 1987 was the year that Country X’s exports 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 exceeded its own imports by the greatest amount. N ow go to the second step. During 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 1987, Country Y’s imports were approximately $35 and Country X’s imports were 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 approximately $13. The difference is $22. Choice (A) is the only one that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 approximates this dollar figure. 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 499

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 8. B The price of two children’s tickets together equals the price of one adult ticket. The 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 total admission price is therefore equivalent to the price of three adult tickets. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3a 5 $12.60 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a 5 $4.20 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Child’s ticket price 5 ~$4.20! 5 $2.10 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 9. E The other integer is n 1 2. The difference between n and (n 1 2) must be positive, so 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the term (n 1 2) must appear first in the equation. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 10. E Convert the question into an algebraic equation, and solve for x : 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 P 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ~x ! M 5 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 100 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 100 5 Px 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 100M 6 123456789012345678901234567890121234567890123456789012345678901212345 5x 6 123456789012345678901234567890121234567890123456789012345678901212345 P 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 11. B The length of each side of the square is 12 feet. The length of the remaining two sides 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 1 6 123456789012345678901234567890121234567890123456789012345678901212345 of the triangle totals 16 feet. The perimeter of the semicircle 5 pd 5 p~12! 5 6p. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 The length of the two sides of the square included in the overall perimeter totals 24. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The total perimeter of the floor 5 16 1 6p 1 24 5 40 1 6p. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 12. D Apply the defined operation to each of the two expressions as follows: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ~4N3N5! 5 12 2 5 5 7 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (6N5N7) 5 30 2 7 5 23 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Then add the two results: 7 1 23 5 30 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 13. B Competitor 1 must engage in eight matches. Competitor 2 must engage in seven 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 matches not already accounted for. (The match between competitors 1 and 2 has 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 already been tabulated.) Similarly, competitor 3 must engage in six matches other 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 than those accounted for, and so on. The minimum number of total matches 5 8 1 7 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 1 5 1 4 1 3 1 2 1 1 5 36. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 14. A Both equations are quadratic. For each one, you can determine the number of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 possible values of x by setting the quadratic expression equal to 0 (zero) and factoring 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that expression. Perform these tasks for equation in statement (1): 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 4x 2 2 4x 5 21 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 4x 2 4x 1 1 5 0 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ~2x 2 1!~2x 2 1! 5 0 6 1 123456789012345678901234567890121234567890123456789012345678901212345 500 12345678901234567890123456789012123456789012345678901234567890121234566

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 As you can see, the equation’s two roots are the same—that is, there’s only one 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 possible value for x . Thus, statement (1) alone suffices to answer the question. N ow 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 perform the same tasks for the equation in statement (2): 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2x 19x 5 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 2x 2 1 9x 2 5 5 0 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ~x 1 5!~2x 2 1! 5 0 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 As you can see, based on the equation given in statement (2), there are two different 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 roots—that is, two possible values of x . Thus, statement (2) alone is insufficient to 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 15. E Cross-multiply to solve for y: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ~9!~y 2 1! 5 ~2y!~3! 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 9y 2 9 5 6y 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3y 5 9 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 y 5 3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 16. D 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The question itself provides that the pitcher currently contains 7 ounces of each 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 brand. Given statement (1), 60% of the 30-quart mixture, or 18 ounces, must be 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 brand A. Subtract 7 from 18 to find the remaining amount of B brand A needed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 (10 ounces). Then subtract 18 from 30 to find the amount of brand B (12). Finally, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 1 1 6 123456789012345678901234567890121234567890123456789012345678901212345 subtract 7 from 12 to find the remaining amount of brand B needed 4 ounces . 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 We’ve answered the question with statement (1) alone. Similarly, statement 2 would 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 lead to the same answer. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 17. A Let x equal the number of nickels: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 45 2 x 5 the number of dimes 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5x 5 the value of all nickels ~in cents! 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 450 2 10x 5 the value of all dimes ~in cents! 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Given a total value of 350 cents: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5x 1 450 2 10x 5 350 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 5x 5 2100 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 5 20 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Lisa has 20 nickels and 25 dimes; thus, she has five more dimes than nickels. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 501

S

D

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 18. D You can organize this problem’s information in a table, as shown in this next figure: 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 male female 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 30% Lange 14% 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 70% Sobel ? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 60% 40% 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Because 35% of 40% of the voters (female) voted for Lange, 14% (.40 3 .35) of all 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 voters were females who voted for Lange. You can now fill in the entire table (the 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 four percentages must total 100% ), as shown in this next figure: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 male female 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Lange 16% 14% 30% 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Sobel 44% 26% 70% 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 60% 40% 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 19. A If Barbara invests x additional dollars at 8% , her total investment will amount to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2,400 1 x ) dollars. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 .05~2,400! 1 .08x 5 .06~2,400! 1 x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5~2,400! 1 8x 5 6~2,400 1 x ! 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 12,000 1 8x 5 14,400 1 6x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2x 5 2,400 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 1,200 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 20. E The total parking fee that ABC pays each month is $1,920 ($240 3 8). O f that 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 amount, $420 is paid for outdoor parking for three cars. The difference ($1,920 2 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 $420 5 $1,500) is the total garage parking fee that the company pays for the other 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 five cars. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 21. A In choice (A), unequal quantities are subtracted from equal quantities. The 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 differences are unequal, but the inequality is reversed because unequal numbers are 6 6 123456789012345678901234567890121234567890123456789012345678901212345 being subtracted from, rather than added to, the equal numbers. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 502 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 22. E Statement (1) alone is insufficient to answer the question, since it provides no 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 information about a or b. M any test-takers would conclude incorrectly that 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) alone is sufficient to answer the question. (About half of these 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 test-takers would assert that the answer to the question is no, while the other half 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 would claim that the answer to the question is yes.) Both groups would be wrong, of 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 course. If c , 0, then dividing c by unequal quantities does not change the inequality. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 But if c . 0, dividing c by unequal quantity reverses the inequality. If you’re the least 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 bit unsure about this, it’s a good idea to plug in a few simple numbers. For example, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 c c 1 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 let a 5 2 and b 5 1. If c 5 1 (a positive value), then , because , . But if 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a b 2 1 6 123456789012345678901234567890121234567890123456789012345678901212345 c 1 1 c 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 c 5 21 (a negative number), then . because 2 . 2 . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a b 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 23. C Statement (1) alone is insufficient to answer the question because it fails to indicate 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 what percent a 10 cent increase amounts to. Statement (2) alone is insufficient 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 because it fails to provide any information as to the change in sales resulting from an 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 increased price. Together, however, statements (1) and (2) provide the information 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 needed. You do not need to calculate the percent decrease in sales; you know that the 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 correct answer is (C). H ere’s how you would perform the calculation, however: A 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 60-cent increase is 6 increases of 10 cents, so the decrease in sales is 30% (6 3 5). 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 24. D Statement (1) establishes a linear equation in one variable: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 x 1 (x 1 1) 5 @~x 1 3! 1 ~x 1 6!#. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 You can determine the second term by solving for x , and statement (1) suffices to 6 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. [The second term is 4.5 (x 5 3.5); however, you need not 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 determine these values.] Statement (2) also establishes a linear equation in one 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 variable: (x 1 15) 1 (x 1 21) 5 43. The seventh term must be (x 1 21) because each 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 successive term in the sequence adds to x a number that is one greater than the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 number that the previous term added to x . Statement (2) alone suffices to answer the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 question. (Again, x 5 3.5 and the second term is 4.5, although you need not 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 determine either value.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 25. B Statement (1) alone allows for more than one possible area, as illustrated below: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) alone, however, allows for only one possible area (and shape and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 position) of the triangle—the one illustrated in diagram (A) above. Thus, statement 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) alone is sufficient to answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 503

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 26. C It’s obvious that neither statement (1) nor (2) alone provides sufficient information to 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 determine the degree measure of ∠x . Thus, you can easily eliminate choices (A), (B), 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 and (D). N ext, consider statements (1) and (2) together. N otice that ∠y and ∠z 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 together form an angle whose degree measure exceeds 180 (a straight line) by x . 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Thus, y 1 z 2 x 5 180. Statements (1) and (2) provide the values of y and z and thus 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 suffice to answer the question (x 5 50). 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 27. E Given x y , 0, either x or y (but not both) must be negative. Despite this restriction, 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 statement (1) alone is insufficient to answer the question because it specifies one equa- 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 tion in two variables. Statement (2) alone is also insufficient. Although x must equal 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 either 22 or 21 (x must be a negative integer), y could be any positive integer. N ow, 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 consider statements (1) and (2) together. Since there are two possible values of x (22 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and 21) in the equation x 1 y 5 2, the difference between x and y could be either 4 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 or 6. Thus, statements (1) and (2) together are insufficient to answer the question. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 28. D Equate the proportions of the negative with those of the printed picture: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 7 6 123456789012345678901234567890121234567890123456789012345678901212345 2 1 6 123456789012345678901234567890121234567890123456789012345678901212345 2 8 6 123456789012345678901234567890121234567890123456789012345678901212345 5 6 123456789012345678901234567890121234567890123456789012345678901212345 4 x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5 15 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 8 6 123456789012345678901234567890121234567890123456789012345678901212345 5 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4 x 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5 15 6 123456789012345678901234567890121234567890123456789012345678901212345 5 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5x 5 15 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 53 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 29. C A C is a diagonal of the square A BCD . To find the length of any square’s diagonal, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2. So first you need to find the length of a side. multiply the length of any side by = 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 H alf the length of a side equals the circle’s radius, and the perimeter of any circle 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 equals 2pr, where r is the radius. Thus, the radius here is 8, and the length of each of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the square’s sides is 16. Therefore, the length of diagonal A C 5 16 2 = 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 30. D The two greatest two-month percent increases for City X were from 1/1 to 3/1 and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 from 5/1 to 7/1. Although the temperature increased by a greater amount during the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 latter of these two periods, the percent increase was greater from 1/1 to 3/1. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 January–February: from 30 degrees to 50 degrees, a 66% increase 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 M ay–June: from 60 degrees to 90 degrees, a 50% increase 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 During the period from 1/1 to 3/1, City Y’s average daily temperature was midway 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 between its highest and lowest temperatures (between 66 degrees and 62 degrees), or 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 about 64 degrees. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 504 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 31. C The only two-month periods in which City Y’s temperature was increasing while City 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 X’s was decreasing were September–O ctober and N ovember–December. Compare 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the two midpoints of the line segments for each period: 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 September–O ctober: City X’s average was 50 and City Y’s was 46. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N ovember–December: City X’s average was 36 and City Y’s average was 60. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 For each city, find the average of the two midpoints: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 50 1 36 6 123456789012345678901234567890121234567890123456789012345678901212345 5 43 City X’s average: 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 46 1 60 6 123456789012345678901234567890121234567890123456789012345678901212345 5 53 City Y’s average: 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 City Y’s average overall temperature was about 10 degrees greater than City X’s 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 during these four months. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 32. D The diagonal of a square is the hypotenuse of a 1:1:=2 right triangle where the two 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 legs are sides of the square. Given a hypotenuse of 8, the length of each side of the 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 8 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 square is , or 4 =2. Accordingly, the square’s perimeter 5 4 3 4 =2 5 16=2. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 =2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 33. E You can express the distance both in terms of Dan’s driving time going home and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 going back to college. Letting x equal the time (in hours) it took Dan to drive home, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 you can express the distance between his home and his workplace both as 60x and as 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 50 (x 1 1). Equate the two distances (because distance is constant) and solve for x as 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 follows: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 60x 5 50~x 1 1! 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 60x 5 50x 1 50 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 55 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 It took Dan five hours at 60 miles per hour to drive from college to home, so the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 distance is 300 miles. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 34. B Combine the terms under the radical into one fraction: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 y2 9y 2 2 y 2 8y 2 4y 2 y2 6 123456789012345678901234567890121234567890123456789012345678901212345 2 5 5 5 6 123456789012345678901234567890121234567890123456789012345678901212345 2 18 18 18 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Then factor out “ perfect squares” from both numerator and denominator: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4y 2 2y 6 123456789012345678901234567890121234567890123456789012345678901212345 5 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 9 3 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 505

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Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 35. C To answer the question, you need to compare the volume of the cylindrical tank with 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the volume of a cube-shaped tank. Statement (1) fails to provide sufficient 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 information to determine these volumes. The volume of the cylindrical tank is 7.5pr2 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 and, given statement (1), you can express the cube’s volume as r3 . The ratio of the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 two volumes, then, is 7.5pr2 : r3 , or 7.5p : r. Accordingly, the comparative volumes of 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the containers vary, depending on the value of r. Statement (2) is also insufficient to 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer the question. Given statement (2), the length of a cube’s side is 2.5 feet, and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 you can determine its volume (s ). H owever, you cannot determine the cylindrical 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 tank’s volume because the size of its circular base remains unknown. Statement (1) 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 provides this missing information. Thus, statements (1) and (2) together suffice to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. Given statements (1) and (2), the ratio of V [cylinder] to V 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 [cube] is 3p: 1, so 10 cube-shaped tanks are required. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 36. B You could solve the problem algebraically by using the arithmetic-mean formula (x is 6 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the seventh number): 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 86 1 82 1 90 1 92 1 80 1 81 1 x 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 84 5 6 123456789012345678901234567890121234567890123456789012345678901212345 7 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 There’s a quicker way, however. 86 is 2 above the 84 average, and 82 is two below. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 These two numbers “ cancel” each other. 90 is 6 above and 92 is 8 above the average 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (a total of 14 above), while 80 is 4 below and 81 is 3 below the average (a total of 7 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 below). Thus, the six terms average out to 7 above the average of 84. Accordingly, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 seventh number is 7 below the average of 84, or 77. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 37. E You can solve this problem by working backward from the answer choices—trying 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 out each one in turn. O r, you can solve the problem algebraically. You can express the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 amount of sugar after you add water as .05(60 1 x ), where 60 1 x represents the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 total amount of solution after you add the additional water. This amount of sugar is 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the same as (equal to) the original amount of sugar (20% of 60). Set up an equation, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 multiply both sides by 100 to remove the decimal point, and solve for x : 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5~60 1 x ! 5 1,200 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 300 1 5x 5 1,200 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5x 5 900 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 180 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 1. B The original version (A) is faulty in two respects. First, the plural subject benefits is 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 followed by the singular verb is. Second, the preposition by is not idiomatic in this 6 123456789012345678901234567890121234567890123456789012345678901212345 context. (B) remedies both problems with the original sentence—by using the plural 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 are, which agrees with benefits, and by replacing by with from (which is 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 idiomatic here). 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 506 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2. C The original statement (A) includes an ambiguous pronoun reference. It is unclear 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 whether they refers to the bounty hunters, their captives, or the authorities. (C) 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 remedies the original sentence’s ambiguous pronoun reference by reconstructing the 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 sentence. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 3. B The original sentence (A) suffers from faulty parallelism. Each of the three items in 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 the underlined clause should be similar in grammatical construction. While actors 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and m usicians both describe the celebrities themselves, som e other high-profile 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 vocation does not. (B) establishes a consistent (parallel) grammatical construction 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 among the three items in the series; each of the three items refers clearly to a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 vocation. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 4. D The claim (in the second sentence) relies on the assumption that all other factors in 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 weight loss—such as exercise and dietary habits—remained unchanged from prior to 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the two-week period through the two-week period. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. B The passage draws the general conclusion that home buyers should “ always” buy a 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 new house based on a few specific advantages that new houses offer. (B) is the best 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 criticism of the argument because it suggests that these factors are not necessarily the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 only factors, or the most important ones, in the home-buying decision. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6. D In the first paragraph, the author cites certain erroneous assumptions upon which the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 U.S. N ew Town concept was based. Then, in the next two paragraphs, the author 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 describes how and why N ew Towns in the United States failed to solve urban 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 problems and to provide the sort of social environment hoped for. (D) provides a 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 good recapitulation of this entire discussion. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 7. E In the second paragraph, the author states that one of the effects of N ew Towns was 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to draw high-income citizens away from the cities—essentially what (E) indicates. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 8. C According to the first sentence of the passage, N ew Towns were originally 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 conceptualized as a way to absorb growth. Based on other information in the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 passage, it appears that U.S. N ew Towns achieved this objective—at least to some 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 extent—since city residents who could afford to move away from urban centers did 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 so. At the same time, however, the cities were left with new problems, such as an 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 insufficient tax base to support themselves and to retain businesses. Thus, like the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 phenomenon that (C) describes, N ew Towns were a new innovation that served to 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 solve one problem but created another along the way. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 9. D The original sentence (A) suffers from faulty parallelism. The second occurrence of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from should be deleted to restore the proper parallelism between the phrases the host 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and the diplom at’s. At the same time, the word both is redundant in light of the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 words the other at the end of the sentence, thereby confusing the meaning of the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 sentence. (D) remedies the original sentence’s faulty parallelism by reconstructing the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 phrase, using the subjunctive form (that . . . be). 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 507

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 10. E If the statement in (E) is true, it suggests that Company X’s experience is comparable 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to that of other merging companies, and therefore it is unlikely that many more 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Company X workers will leave as a result of the merger. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 11. A Gwen’s argument relies on the assumption that expensive restaurants are not as 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 popular among the college students as inexpensive restaurants. Jose provides one 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 reason why expensive restaurants are not necessarily less popular among the college 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 students, suggesting that the disagreement is about whether expensive restaurants are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 in fact less popular among the college students than inexpensive ones. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 12. A The original version is the best one. The noun clause w hether the universe is bound is 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 properly considered the subject of the sentence. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 13. E The original sentence (A) improperly uses less instead of few er in reference to a 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 numerical quantity (the number of chemicals tested). Also, the modifier m ost of 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 w hich is separated from its antecedent (thirty), resulting in confusion as to whether 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 m ost of w hich refers to the thirty chemicals tested or the tests themselves. (E) 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 remedies both problems in the original sentence. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 14. A The original sentence (A) correctly uses the singular pronoun its in referring to the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 singular bureaucracy. Also, (A) is consistent in its use of the future tense. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 15. C The passage describes an imaginary debate over the American democratic ideal 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 among the writers of the American Renaissance, in which Emerson, Thoreau, and 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Whitman are grouped together in one school of thought while H awthorne and 6 123456789012345678901234567890121234567890123456789012345678901212345 M elville are paired in another. Choice (C) nicely matches this recap. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 16. E The passage is clear throughout that Emerson is an idealist, which is just the opposite 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of a pragmatist. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 17. D According to the passage, M elville, through his story of Pierre, conveyed the notion 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 that democratic idealism was based on “ misguided assumptions.” Although the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 author is not as explicit that H awthorne also believed idealists to be misguided, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 H awthorne’s conclusion that transcendental freedom leads to moral anarchy can 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonably be interpreted this way. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 18. C The argument’s conclusion is that the new lifeguard was not a factor in the declining 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 number of deaths from last year to this year. (C) rules out one other possible 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 explanation for the decline in the number of drownings, in turn rendering it more 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 likely that the additional lifeguard did contribute to the decline. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 19. E The conclusion in (E) is logically inferable from two premises given in the passage: (1) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 If M etaCorp continues to show a profit, then analysts will continue to recommend it 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (in symbolic form: If A , then B), and (2) if analysts recommend M etaCorp stock, then 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the stock’s price will at least remain at its current level—in other words, either remain 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the same or increase (in symbolic form: If B, then C). From these two premises, (E) is 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 logically inferable (in symbolic form: If A , then C). 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 508 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 20. A The argument that the public is interested in high culture relies on the assumption 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that opera, ballet, or classical music are considered “ high culture.” (A) provides some 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 evidence that this necessary assumption is a questionable one. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 21. A The discrepancy among the cited studies involves the increase in the level of violence 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 in television programming over the last twenty years. O ne possible explanation for 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 the discrepancy is that the recent studies relied on different previous studies, which 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 disagreed as to what the level was twenty years ago. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 22. E The original version improperly uses derive instead of the proper idiom are derived 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 from . (E) corrects this diction error. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 23. E The original sentence (A) is faulty in its use of the pronoun them instead of the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 possessive their where the object of a verb (opposed) is a gerund (trivializing) that it is 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 not the musicians themselves but, instead, their actions or traits. (E) corrects the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 improper use of them , replacing it with the possessive their, which properly precedes 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the gerund trivializing. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 24. A The original sentence (A) is correct in its use of the idiomatic phrase have yet to. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 25. B The factual information cited in the passage suggests that eating high-fat foods does 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 not cause obesity. H owever, that information is no help in determining the real cause. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 By showing that the rise in obesity has coincided with an increase in the sales of 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 high-sugar foods, (B) suggests that excessive sugar consumption might be the cause. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Although this correlation in itself does not irrefutably prove that sugar is the culprit, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 it nevertheless helps strengthen the case. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 26. C The argument’s first sentence suggests that the supply-demand ratio for rental 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 apartments with two or more bedrooms is decreasing at a faster rate than the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 supply-demand ratio of rental apartments with one or fewer bedrooms. O ne possible 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 explanation for the difference is the one that (C) provides. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 27. D The original version (A) is faulty in two respects. First, the placement of the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 commas sets up a flawed parallel structure between the progressive verbs w as 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 considered and w ill be considered. Second, the phrase considered as is idiomatically 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 questionable here. A person is considered or considered to be, not considered as, at 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 least in the broader context of this sentence. (D) remedies both problems with the 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 original sentence. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 28. B According to the passage, all cells of an organism contain the same genotype as the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fertilized egg (lines 13–14). Thus, (B) contradicts the information in the passage. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 29. E According to the passage, the maternal programming of early development and the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 genomic control of later differentiation are “ especially well documented” (line 43). 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 509

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 30. A In the first two paragraphs, the author discusses the process of cell differentiation in 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 embryonic development. While the author is particularly concerned with examining 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the mechanisms involved, no specific type of organism (animal) is discussed as an 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 illustration until the final paragraph (which focuses on the sea urchin). Accordingly, 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (A) properly reflects the flow of the author’s discussion. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 31. B It allows you to confidently conclude that biotechnology firms will in fact continue to 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 replace equipment more frequently than other businesses, and therefore will stand to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 benefit from the proposed law more than other businesses. It would make sense, then, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that the biotechnology lobbyists might be behind the proposal. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 32. D It would reduce the number of options available to new college graduates, thereby 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 12 increasing the likelihood that a new college graduate would enter one of the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 lower-paying professions that requires only a four-year degree. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 33. B The original sentence awkwardly mixes the active voice (first clause) and the passive 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 voice (second clause). It also includes the unnecessarily wordy by w ay of. (B) corrects 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 both problems with a concise second clause in the active voice. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 34. D The original sentence (A) misplaces the phrase Even for high school freshm en and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 sophom ores. This phrase is intended to modify m any students; therefore, the author 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 should reconstruct the sentence so that the two phrases appear nearer to each other. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (D) moves the initial phrase to the end of the sentence, clarifying the sentence’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 meaning. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 35. E The argument suggests that the key to a third-world country’s political stability is to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 afford its citizens certain powers. H owever, the argument relies entirely on one 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 observed case (Country X) in which both characteristics are present. To be 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 convincing, the argument must at least show that these powers actually contributed 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 to Country X’s political stability. (E) provides one plausible scenario in which these 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 powers could have nothing to do with the country’s political stability. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 36. A It is reasonably inferable from the first paragraph as a whole that the “ standard 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 repertory” mentioned in lines 13–14 refers to the music of Bach and Telemann as well 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 as to other (“ modern” ) music from their time (first half of the eighteenth century). In 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the second paragraph, the author mentions that the music of Bach, Telemann, and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 their contemporaries called for obsolete instruments (lines 32–34). Thus, the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 standard repertory might have included music that called for the use of obsolete 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 instruments, as response (E) indicates. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 37. D Although the passage does indicate that early music often called for the use of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 obsolete instruments, the passage does not state explicitly that performance practice 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 involved determining which musical instrument to use. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 510 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 38. B According to the passage, the German musicologists did not study the music of 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M ozart and H aydn (post-1750 music) because, among other reasons, their music, 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 “ having never ceased to be performed, had maintained some kind of oral tradition of 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 performance practice” (lines 48–50). Unannotated music is music that is not written, 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 but strictly oral. (B) restates the author’s point in these lines. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 39. C According to the passage, performance practice was developed alongside the modern 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (early twentieth-century) collegium musicum, which was part of the German 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 university. While the modern collegium musicum performed music from before the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 time of Bach and H andel, scholars in the field of performance practice studied certain 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 aspects (e.g., choice of instruments, deciphering notation) of music from the same 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 time period. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 40. C If there are other ways to prevent one’s cat from accumulating hairballs, then there is 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 no reason to risk the cat’s developing an allergic reaction (and, in turn, a harmful 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 infection) by feeding it the medicated food. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 41. C The original sentence (A) contains a misplaced modifying phrase (following the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 comma). The sentence’s construction suggests that it is the electorate that cannot 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonably be disputed, although this makes little sense in the context of the sentence 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 as a whole. (C) remedies the underlined phrase’s faulty construction by rephrasing it 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 as a noun clause. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 511

Practice Test

2 1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Analysis of an Issue 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 Question—30 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose a response to the following statement and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 “ N o business should sacrifice the quality of its products or services for the sake of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 maximizing profits.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Discuss the extent to which you agree or disagree with the foregoing statement. Support your 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 perspective using reasons and/or examples from your experience, observation, reading, or 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 academic studies. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 Question—30 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose an essay for the following argument and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The following is excerpted from an editorial appearing in a local newspaper: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 “ In order to prevent a decline of O ak City’s property values and in rents that O ak City 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 property owners can command, the residents of O ak City must speak out against the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 approval of a new four-year private college in their town. After all, in the nearby town of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 M apleton the average rent for apartments has decreased by ten percent since its new 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 community college opened last year, while the average value of M apleton’s single-family 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 homes has declined by an even greater percentage over the same time period.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 512

TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Discuss how well reasoned you find this argument. In your discussion be sure to analyze the line 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of reasoning and the use of evidence in the argument. For example, you may need to consider 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 what questionable assumptions underlie the thinking and what alternative explanations or 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 counterexamples might weaken the conclusion. You can also discuss what sort of evidence 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 would strengthen or refute the argument, what changes in the argument would make it more 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 logically sound, and what, if anything, would help you better evaluate its conclusion. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 Quantitative Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 37 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Problem Solving Questions: (T hese directions w ill appear on your 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 screen before your first Problem Solving question.) 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Solve this problem and indicate the best of the answer choices given. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 N umbers: All numbers used are real numbers. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Problem Solving question is intended to provide infor6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 mation useful in solving the problem. Figures are drawn as accurately as possible EXCEPT 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 when it is stated in a specific problem that its figure is not drawn to scale. Straight lines 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 may sometimes appear jagged. All figures lie on a plane unless otherwise indicated. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Data Sufficiency Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first D ata Sufficiency question.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 This Data Sufficiency problem consists of a question and two statements, labeled (1) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and (2), in which certain data are given. You have to decide whether the data given in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the statements are sufficient for answering the question. Using the data given in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 statements plus your knowledge of mathematics and everyday facts (such as the num123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ber of days in July or the meaning of counterclock w ise), you must indicate whether: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statement (1) ALO N E is sufficient, but statement (2) alone is not sufficient to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 answer the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) ALO N E is sufficient, but statement (1) alone is not sufficient to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 answer the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 BO TH statements (1) and (2) TO GETH ER are sufficient to answer the question 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 asked; but N EITH ER statement ALO N E is sufficient; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 EACH statement ALO N E is sufficient to answer the question asked; 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statements (1) and (2) TO GETH ER are N O T sufficient to answer the question 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 asked, and additional data specific to the problem are needed. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 513

Part V: T hree Practice Tests

N ote

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N umbers: All numbers used are real numbers. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Data Sufficiency problem will conform to the informa2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tion given in the question, but will not necessarily conform to the additional information 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in statements (1) and (2). 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Lines shown as straight can be assumed to be straight and lines that appear jagged can also 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be assumed to be straight. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 You may assume that positions of points, angles, regions, etc., exist in the order shown and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that angle measures are greater than zero. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 All figures lie in a plane unless otherwise indicated. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N ote: In Data Sufficiency problems that ask you for the value of a quantity, the data given 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in the statements are sufficient only when it is possible to determine exactly one numerical 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 value for the quantity. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Although the questions in this section cover all difficulty levels, you’ll find fewer easy 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 questions than challenging ones. Keep in mind that the GM AT CAT will determine the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 difficulty level of each question based on your responses to prior questions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3 3. H ow many buses are required to transport 6 1. What is the sum of =.49, , and 80% ? 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 4 175 students to the museum? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. .425 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) N o two buses have the same carrying 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 1.59 6 123456789012345678901234567890121234567890123456789012345678901212345 capacity. 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 1.62 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) The average capacity of a bus is 55 D. 2.04 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 students. E. 2.25 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. The storage capacity of disk drive A is 6 123456789012345678901234567890121234567890123456789012345678901212345 2. If the value of X Y Z Company stock drops 6 123456789012345678901234567890121234567890123456789012345678901212345 85% that of disk drive B. What percent6 123456789012345678901234567890121234567890123456789012345678901212345 from $25 per share to $21 per share, what 6 123456789012345678901234567890121234567890123456789012345678901212345 age of drive B’s storage capacity is is the percent of decrease? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 currently used? 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 4 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) Disk drive B holds 3 more gigabytes B. 8 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 than disk drive A. C. 12 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 16 123456789012345678901234567890121234567890123456789012345678901212345 (2) 8.5 gigabytes of disk drive B’s storage 6 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 20 6 123456789012345678901234567890121234567890123456789012345678901212345 capacity is currently used. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 514 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 8 and 9 refer to the following graph: 6 5. Eight square window panes of equal size 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are to be pieced together to form a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 rectangular French door. What is the 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 perimeter of the door, excluding framing 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 between and around the panes? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) The area of each pane is 1 square foot. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) The area of the door, excluding 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 framing between and around the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 panes, is 8 square feet. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6. The denominator of a certain fraction is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 twice as great as the numerator. If 4 were 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 added to both the numerator and denomi3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 nator, the new fraction would be . What 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 8 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is the denominator of the fraction? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 3 6 123456789012345678901234567890121234567890123456789012345678901212345 8. By approximately how many square feet 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 does the size of Unit A exceed that of Unit 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 9 6 123456789012345678901234567890121234567890123456789012345678901212345 C? 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 12 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 13 A. 9,000 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 11,000 6 123456789012345678901234567890121234567890123456789012345678901212345 7. If .2t 5 2.2 2 .6s and .5s 5 .2t 1 1.1, 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 12,500 6 123456789012345678901234567890121234567890123456789012345678901212345 then s 5 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 15,500 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 19,000 A. 1 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 3 6 123456789012345678901234567890121234567890123456789012345678901212345 9. The combined area of Unit B and Unit D 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 10 6 123456789012345678901234567890121234567890123456789012345678901212345 is approximately 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 11 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 30 A. 51,000 square feet. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. 57,500 square feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 70,000 square feet. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 74,500 square feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 108,000 square feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 515

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 10. Carrie’s current age is 24 years greater 13. If the average (arithmetic mean) of the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 than her son Benjamin’s age. In 8 years, first sixteen positive integers is subtracted 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Carrie’s age will be twice Benjamin’s age from the average (arithmetic mean) of the 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 at that time. What is Carrie’s current age? next sixteen positive integers, what is the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 result? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 32 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. 40 A. 0 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 48 B. 16 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 52 C. 32 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 66 D. 64 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 128 6 123456789012345678901234567890121234567890123456789012345678901212345 11. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 14. If a . b, and if c . d, then 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. a 2 b . c 2 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. a 2 c . b 2 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. c 1 d , a 2 b 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. a 2 c , b 1 d 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. b 1 d , a 1 c 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 15. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 In the figure above, if the length of D C is 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 12, what is the area of A BCD ? A closed cardboard box is to be designed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for packing the cylindrical tube shown 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 99 6 123456789012345678901234567890121234567890123456789012345678901212345 above. Will the entire tube fit inside the 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 108 6 123456789012345678901234567890121234567890123456789012345678901212345 box? C. 112 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 120 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) The empty box contains 3 cubic feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 50 =3 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) The total surface area of the box is 14 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 square feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 3 7 5 6 123456789012345678901234567890121234567890123456789012345678901212345 12. =81x 2 =162x 5 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 16. If x and y are negative integers, and if 9x 27x = = 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 2 y 5 1, what is the least possible value 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 3 of x y? A. 3x 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 0 3 6 123456789012345678901234567890121234567890123456789012345678901212345 B. =2x 2 3 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 1 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 2 C. 3x 2 3 =2x 6 123456789012345678901234567890121234567890123456789012345678901212345 = D. 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 3x 2 2 =2 E. 4 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 9x 2 =3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 516 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 17. A certain jar contains 20 jellybeans; each 21. If a computer dealer bought a particular 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 jellybean is either black, pink, or yellow. computer system for $10,000 and sold the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Does the jar contain more pink jellybeans computer system to a customer, how much 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 than yellow jellybeans? did the customer pay for the computer 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 system? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) The jar contains more black jellybeans 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 than pink jellybeans. (1) The dealer’s profit from the sale was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 50% . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) The jar contains 6 pink jellybeans. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 (2) The amount that the dealer paid for 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 18. Is the value of a 2 b greater than the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the computer system was two-thirds 3456789012345678901234567890121234567890123456789012345678901212345 6 12 value of (3a 1 3b)(2a 2 2b)? 123456789012345678901234567890121234567890123456789012345678901212345 the amount that the customer paid for 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the computer system. (1) b , a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) a , 21 22. Which of the following distributions of 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 numbers has the greatest standard 6 123456789012345678901234567890121234567890123456789012345678901212345 19. If b x c 5 (x 1 2) 2 (x 1 1) 2 (x 2 1) 6 123456789012345678901234567890121234567890123456789012345678901212345 deviation? 6 123456789012345678901234567890121234567890123456789012345678901212345 2 (x 2 2), what is the value of b 2100 c 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. {23, 1, 2} 2 b 100 c? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. {22, 21, 1, 2} 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 2196 6 123456789012345678901234567890121234567890123456789012345678901212345 C. {3, 5, 7} 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 21 6 123456789012345678901234567890121234567890123456789012345678901212345 D. {21, 2, 3, 4} 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 0 6 123456789012345678901234567890121234567890123456789012345678901212345 E. {0, 2, 4} 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 400 23. Patrons at a certain restaurant can select 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 two of three appetizers—fruit, soup, and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 20. 123456789012345678901234567890121234567890123456789012345678901212345 salad—along with two of three veg123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 etables—carrots, squash, and peas. What 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is the statistical probability that any 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 patron will select fruit, salad, squash, and 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 peas? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 6 123456789012345678901234567890121234567890123456789012345678901212345 12 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 6 123456789012345678901234567890121234567890123456789012345678901212345 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 In the figure above, if PQ R S is a rectangle, 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 and if the length of Q R is 12, is PQ R S a 1 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 square? 6 123456789012345678901234567890121234567890123456789012345678901212345 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) The length of SQ is 12 =2. 1 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 (2) The length of PS is 12. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 517

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 24. If bin A contains exactly twice as many 28. If x . 0, and if x 1 3 is a multiple of 3, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 potatoes as bin B, and if bin A contains which of the following is not a multiple 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 exactly 11 more potatoes than bin C, does of 3? 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 bin B contain more potatoes than bin C? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) The difference between the number of B. x 1 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 potatoes in bin C and the number in C. 3x 1 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 bin A is greater than the number of D. 2x 1 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 potatoes in bin B. E. 6x 1 18 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) If one potato were added to bin A and 3456789012345678901234567890121234567890123456789012345678901212345 6 29. If one dollar can buy m pieces of paper, 12 6 123456789012345678901234567890121234567890123456789012345678901212345 to bin C, bin A would contain exactly how many dollars are needed to buy p 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 twice as many potatoes as bin C. reams of paper? (N ote: 1 ream 5 500 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pieces of paper.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 25. O ne of two ropes equal in length is cut 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 into three segments to form the largest 6 123456789012345678901234567890121234567890123456789012345678901212345 p 6 123456789012345678901234567890121234567890123456789012345678901212345 A. possible triangular area. The other rope is 6 123456789012345678901234567890121234567890123456789012345678901212345 500m 6 123456789012345678901234567890121234567890123456789012345678901212345 cut into four segments to form the largest 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 m possible rectangular area. Which of the 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 6 123456789012345678901234567890121234567890123456789012345678901212345 following most closely approximates the 500p 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ratio of the triangle’s area to the rectan6 123456789012345678901234567890121234567890123456789012345678901212345 500 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 gle’s area? 6 123456789012345678901234567890121234567890123456789012345678901212345 p 1 m 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 1:2 500p 6 123456789012345678901234567890121234567890123456789012345678901212345 D. B. 2:3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 m C. 3:4 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 500m (p 2 m ) D. 1:1 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 4:3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 26. Code letters X , Y , and Z each represent 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 one digit in the three-digit prime number 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 X Y Z . If neither X nor Y is an odd integer, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 what is the number represented by X Y Z ? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) The sum of the three digits is 7. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) X 2 Y . 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 27. If abcd Þ 0, and if 0 , c , b , a , 1, is 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 a bc 6 123456789012345678901234567890121234567890123456789012345678901212345 it true that 2 , 1? 6 123456789012345678901234567890121234567890123456789012345678901212345 d 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) a 5 =d 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) d . 0 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 518 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 32. Questions 30 and 31 refer to the following 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 chart: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 O n the x y-plane above, if the equation of 6 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 l x and if point B is defined by the is y5 1 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x y-coordinate pair (5,0), what is the area 6 123456789012345678901234567890121234567890123456789012345678901212345 30. At the end of September, the combined 6 123456789012345678901234567890121234567890123456789012345678901212345 of DO A B ? 6 123456789012345678901234567890121234567890123456789012345678901212345 share price of Ardent stock and BioFirm 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 4 stock exceeded the share price of Compu6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 3 =2 Win stock by approximately 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. 2 =5 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 20% 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 5 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 35% 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 7 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 50% 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 100% 6 123456789012345678901234567890121234567890123456789012345678901212345 33. Twelve of 28 students are enrolled in 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 150% 123456789012345678901234567890121234567890123456789012345678901212345 English Literature, while 9 are enrolled in 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 World H istory. H ow many of the 28 31. During which of the following months did 6 123456789012345678901234567890121234567890123456789012345678901212345 students are enrolled in Algebra I? 6 123456789012345678901234567890121234567890123456789012345678901212345 the aggregate share price of stock in all 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 three companies change the LEAST? (1) Three of the 28 students are enrolled 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in English Literature and World 6 123456789012345678901234567890121234567890123456789012345678901212345 A. July 6 123456789012345678901234567890121234567890123456789012345678901212345 H istory but not Algebra I. 6 123456789012345678901234567890121234567890123456789012345678901212345 B. August 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. O ctober (2) The total enrollment of all three 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. N ovember classes is 35. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. December 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 519

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 37. A legislature passed a bill into law by a 34. Total revenue from the sale of adult and 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 5:3 margin. N o legislator abstained. What 6 student tickets was $180. If twice as many 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 part of the votes cast were cast in favor of 6 student tickets as adult tickets were sold, 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 the motion? and if 27 tickets were sold altogether, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 what was the total revenue from the sale 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 6 123456789012345678901234567890121234567890123456789012345678901212345 of student tickets? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 8 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) The price of each adult ticket was 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 6 123456789012345678901234567890121234567890123456789012345678901212345 $10. 5 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) The price of each student ticket was 8 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 50% of the price of each adult ticket. 15 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 35. If a, b, c and d are integers, is the sum of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ab and cd an odd integer? 5 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5 (1) a and c are both even integers. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 8 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) b is an even integer and d is an odd 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 integer. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 36. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 As shown in the figure above, from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 runway 1, airplanes must turn either 120° 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to the right onto runway 2 and 135° to the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 left onto runway 3. Which of the follow6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ing does N O T indicate a complete turn 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 from one runway to another? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 30° 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. 55° 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 60° 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 75° 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 105° 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 520 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 41 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Sentence Correction Questions: (T hese directions w ill appear on your 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Sentence Correction question.) 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 This question presents a sentence, all or part of which is underlined. Beneath the sentence 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 you will find five ways of phrasing the underlined part. The first of these repeats the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 original; the other four are different. If you think the original is best, choose the first 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer; otherwise choose one of the others. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 This question tests correctness and effectiveness of expression. In choosing your answer, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 follow the requirements of Standard Written English; that is, pay attention to grammar, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 choice of words, and sentence construction. Choose the answer that produces the most 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 effective sentence; this answer should be clear and exact, without awkwardness, ambigu3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ity, redundancy, or grammatical error. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Critical Reasoning Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Critical R easoning question.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 For this question, select the best of the answer choices given. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Reading Comprehension Questions: (T hese directions w ill appear on 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 your screen before your first group of R eading Com prehension questions.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The questions in this group are based on the content of a passage. After reading the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage, choose the best answer to each question. Answer all the questions following the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage on the basis of what is stated or im plied in the passage. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 521

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 1. Either interest rates or the supply of 4. According to life-insurance company 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 money can, along with the level of statistics, nine out of ten alcoholics die 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 government spending, be factors contribbefore the age of seventy-five, as opposed 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 uting to the amount of monetary inflation. to seven out of ten non-alcoholics. A 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 recent report issued by the State M edical 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. can, along with the level of govern6 123456789012345678901234567890121234567890123456789012345678901212345 Board recounts these statistics and 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 ment spending, be factors contribut3456789012345678901234567890121234567890123456789012345678901212345 6 12 concludes that alcohol addiction increases 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ing to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a person’s susceptibility to life-threatening 6 123456789012345678901234567890121234567890123456789012345678901212345 B. along with the level of government 2 3456789012345678901234567890121234567890123456789012345678901212345 1 diseases, thereby reducing life expectancy. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 spending, can one or the other be 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 contributing factors in The conclusion drawn by the State 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. can, along with the level of governM edical Board depends on which of the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ment spending, contribute as facfollowing assumptions? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tors to A. People who are predisposed to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. can be a contributing factor to, along life-threatening diseases are more 3456789012345678901234567890121234567890123456789012345678901212345 6 12 with the level of government spending 3456789012345678901234567890121234567890123456789012345678901212345 6 12 likely than other people to become 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. can contribute, along with the level of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 alcoholic. 6 123456789012345678901234567890121234567890123456789012345678901212345 government spending, to 6 123456789012345678901234567890121234567890123456789012345678901212345 B. The statistics cited exclude deaths due 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to other alcohol-related events such as 6 123456789012345678901234567890121234567890123456789012345678901212345 2. During his prolific career, Beethoven 6 123456789012345678901234567890121234567890123456789012345678901212345 automobile accidents. 6 123456789012345678901234567890121234567890123456789012345678901212345 composed dozens of symphonies, out of 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Alcoholism does not also increase a 6 123456789012345678901234567890121234567890123456789012345678901212345 which he never completed some of them. 123456789012345678901234567890121234567890123456789012345678901212345 person’s susceptibility to diseases that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. out of which he never completed some are not life-threatening. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of them D. The life expectancy of that portion of 6 123456789012345678901234567890121234567890123456789012345678901212345 B. of which some of them were never 123456789012345678901234567890121234567890123456789012345678901212345 the general population not character- 6 6 123456789012345678901234567890121234567890123456789012345678901212345 completed by him 6 123456789012345678901234567890121234567890123456789012345678901212345 ized by alcoholism increases over 6 123456789012345678901234567890121234567890123456789012345678901212345 C. which some he never completed 6 123456789012345678901234567890121234567890123456789012345678901212345 time. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. some of which he never completed 123456789012345678901234567890121234567890123456789012345678901212345 E. The author of the report is not biased 6 6 123456789012345678901234567890121234567890123456789012345678901212345 E. but some were not completed by him 6 123456789012345678901234567890121234567890123456789012345678901212345 in his or her personal opinion about 6 123456789012345678901234567890121234567890123456789012345678901212345 the morality of alcohol consumption. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3. The space program’s missions to M ars 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 have confirmed that the soil composition 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 on that planet is similar to that on our 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 planet. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. to that on our planet 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. to our planet 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. with the soil on our planet 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. to this composition on our planet 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. to our planet’s soil’s composition 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 522 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 6–8 are based on the following 5. For the purpose of stimulating innovation 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 passage: at TechCorp, one of the company’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 long-standing goals has been to obtain at 6 123456789012345678901234567890121234567890123456789012345678901212345 Line The Pan-American land bridge, or 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 least 50 percent of its annual revenues 3456789012345678901234567890121234567890123456789012345678901212345 6 12 isthmus, connecting N orth and South 3456789012345678901234567890121234567890123456789012345678901212345 6 12 from sales of products that are no more 3456789012345678901234567890121234567890123456789012345678901212345 6 12 America was formed volcanically long 6 123456789012345678901234567890121234567890123456789012345678901212345 than three years old. Last year, TechCorp 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 after dinosaurs became extinct. The 3456789012345678901234567890121234567890123456789012345678901212345 6 12 achieved this goal, despite the fact that the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 isthmus cleaved populations of marine (5) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 company introduced no new products 6 123456789012345678901234567890121234567890123456789012345678901212345 organisms, creating sister species. These 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 during the year. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 twin species, called “ geminates,” then 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Which of the following, if true, best evolved independently. Scientists observe, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 explains the results described above? for example, that Pacific pistol shrimp no 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 longer mate with those from the Atlantic 6 (10) A. N one of the company’s competitors 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 O cean. Yet the two oceans had already introduced any new products during 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 begun to form their distinctive personalithe last year. 6 123456789012345678901234567890121234567890123456789012345678901212345 ties long before the isthmus was fully 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Scientists at the company report that 6 123456789012345678901234567890121234567890123456789012345678901212345 formed. As the seabed rose, Pacific 6 123456789012345678901234567890121234567890123456789012345678901212345 they are close to breakthroughs that 6 123456789012345678901234567890121234567890123456789012345678901212345 waters grew cooler, their upswelling (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 should result in several new products 6 123456789012345678901234567890121234567890123456789012345678901212345 currents carrying rich nutrients, while the 6 123456789012345678901234567890121234567890123456789012345678901212345 during the coming year. 6 123456789012345678901234567890121234567890123456789012345678901212345 Atlantic side grew shallower, warmer, 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Sales of some of the company’s older 6 123456789012345678901234567890121234567890123456789012345678901212345 and nutrient poor. In fact, it was these 6 123456789012345678901234567890121234567890123456789012345678901212345 products were discontinued during 6 123456789012345678901234567890121234567890123456789012345678901212345 new conditions, and not so much the 6 123456789012345678901234567890121234567890123456789012345678901212345 that last year. 6 123456789012345678901234567890121234567890123456789012345678901212345 fully-formed isthmus, that spawned (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The company has introduced very few 6 123456789012345678901234567890121234567890123456789012345678901212345 changes in the shrimp population. 6 123456789012345678901234567890121234567890123456789012345678901212345 new products during the last three 6 123456789012345678901234567890121234567890123456789012345678901212345 For terrestrial life, the impact of the 6 123456789012345678901234567890121234567890123456789012345678901212345 years. 6 123456789012345678901234567890121234567890123456789012345678901212345 isthmus was more immediate. Animals 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Company spending on research and 6 123456789012345678901234567890121234567890123456789012345678901212345 traversed the newly formed bridge in 6 123456789012345678901234567890121234567890123456789012345678901212345 development has increased sharply 6 123456789012345678901234567890121234567890123456789012345678901212345 both directions, although N orth Ameri(25) 6 123456789012345678901234567890121234567890123456789012345678901212345 over the past five years. 123456789012345678901234567890121234567890123456789012345678901212345 can creatures proved better colonizers— 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 more than half of South America’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 mammals trace direct lineage to this 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 so-called Great American Biotic Ex6 123456789012345678901234567890121234567890123456789012345678901212345 change. O nly three animals—the (30) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 armadillo, opossum, and hedgehog— 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 survive as transplants in the north today. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 523

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 8. Which of the following statements is most 6 6. Which of the following statements finds 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 readily inferable from the information in the LEAST support in the passage? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the passage? 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Population divergences resulting from 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Species of marine organisms in the the formation of the Pan-American isth3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Atlantic O cean number fewer today mus were more a process than an event. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 than before the formation of the B. The divergence in ocean temperature 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Pan-American isthmus. during the formation of the Pan3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 B. The number of terrestrial animal speAmerican isthmus resulted in a 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 cies in South America today exceeds divergence in the ocean’s nutrient 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the number prior to the formation of value. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 the Pan-American isthmus. C. Genetic differences among pistol 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. O f the indigenous South American shrimp have grown to the point that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 species that migrated north across the 6 there are now at least two distinct 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Pan-American isthmus, more than species of these shrimp. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 three survive to this day. D. The part of ocean which is now the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. Since the formation of the PanPacific grew deeper due to the 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 American isthmus, fewer terrestrial geologic forces that created the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 animals have traveled north across the Pan-American isthmus. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 isthmus than south. E. N ot until the Pan-American isthmus 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. As the Pan-American isthmus began to was fully formed did geminate marine 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 form, most pistol shrimp migrated organisms begin to develop in that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 west to what is now the Pacific O cean. area of the ocean. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 9. That which is self-evident cannot be 7. The author mentions the mating habits of 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 pistol shrimp in order to show that disputed, and that in itself is self-evident. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. some species of marine organisms A. That which is self-evident cannot be 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 inhabiting the Pacific O cean are now disputed, and that in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 entirely distinct from those in the B. That that is self-evident cannot be 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Atlantic O cean. disputed, of which 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. twin species of marine organisms can C. It is self-evident that which cannot be 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 each survive even though one species disputed, and this fact 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 can no longer mate with the other. D. The self-evident cannot be disputed, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. since the formation of the Panand this fact 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 American isthmus, some marine E. That which is self-evident cannot be 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 geminates no longer mate with their disputed, a fact which 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 sister species. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. geminate species that do not mate 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 with one another are considered 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 separate species. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. the evolutionary impact of the Pan6 123456789012345678901234567890121234567890123456789012345678901212345 American isthmus was greater for ma6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rine organisms than for land animals. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 524 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 11. Very few software engineers have left 10. People who discontinue regular exercise 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M icroFirm Corporation to seek employtypically claim that exercising amounted 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 ment elsewhere. Thus, unless CompTech to wasted time for them. But this claim is 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Corporation increases the salaries of its born of laziness, in light of the over3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 software engineers to the same level as whelming evidence that regular exercise 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 those of M icroFirm’s, these CompTech improves one’s health. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 employees are likely to leave CompTech 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following statements, if true, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 for another employer. 6 123456789012345678901234567890121234567890123456789012345678901212345 would most seriously weaken the argu2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The flawed reasoning in the argument ment above? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 above is most similar to the reasoning in 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Exercise has been shown to not only 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 which of the following arguments? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 improve one’s health, but also to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Robert does not gamble, and he has increase longevity, or life span. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 never been penniless. Therefore, if B. People who have discontinued regular 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Gina refrains from gambling she will 6 exercise now make productive use of 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 also avoid being penniless. the time they formerly devoted to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. If Dan throws a baseball directly at exercise. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the window, the window pane will C. People who are in good health are 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 surely break. The window pane is not 6 more likely to exercise regularly than 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 broken, so Dan has not thrown a people who are in poor health. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 baseball directly at it. D. A person need not exercise every day 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. If a piano sits in a humid room the to experience improved health from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 piano will need tuning within a week. the exercise. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 This piano needs tuning; therefore, it 6 E. People who are in poor health are less 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 must have sat in a humid room for at 6 likely to exercise than other people. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 least a week. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. Diligent practice results in perfection. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Thus, one must practice diligently in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 order to achieve perfection. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. M ore expensive cars are stolen than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 inexpensive cars. Accordingly, owners 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of expensive cars should carry auto 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 theft insurance, whereas owners of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 inexpensive cars should not. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 525

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 14. In 19th-century Europe, a renewed 12. The technique of “ ping-ponging,” which 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 interest in M iddle Eastern architecture permits overdubbing of audio sound 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 was kindled not only by increased trade tracks, has not been used as much from 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 the time of the advent of computer-based but also by increased tourism and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 recording. improved diplomatic relations. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 A. as much from the time of A. not only by increased trade but also 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. as much since by 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 C. as much as B. by not only increased trade but also 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. much as after by 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. much because of C. not only by increased trade but also 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. not only by increased trade but 3456789012345678901234567890121234567890123456789012345678901212345 6 12 13. The volatility of a balanced portfolio of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. by increased trade and also by 3456789012345678901234567890121234567890123456789012345678901212345 6 12 stocks and bonds, less than eighty percent 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of the overall stock market. 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 15–17 are based on the following 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 passage: A. The volatility of a balanced portfolio 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of stocks and bonds, less than eighty 6 123456789012345678901234567890121234567890123456789012345678901212345 Line H istorians sometimes forget that no 6 123456789012345678901234567890121234567890123456789012345678901212345 percent of the overall stock market. 6 123456789012345678901234567890121234567890123456789012345678901212345 matter how well they might come to 6 123456789012345678901234567890121234567890123456789012345678901212345 B. A balanced portfolio of stocks and 123456789012345678901234567890121234567890123456789012345678901212345 know a particular historical figure, they 6 6 123456789012345678901234567890121234567890123456789012345678901212345 bonds is less than eighty percent as 123456789012345678901234567890121234567890123456789012345678901212345 are not free to claim a godlike knowledge 6 6 123456789012345678901234567890121234567890123456789012345678901212345 volatile as the overall stock market. 123456789012345678901234567890121234567890123456789012345678901212345 of the figure or of the events surrounding 6 (5) 6 123456789012345678901234567890121234567890123456789012345678901212345 C. A balanced portfolio of stocks and 6 123456789012345678901234567890121234567890123456789012345678901212345 the figure’s life. Richard III, one of 6 123456789012345678901234567890121234567890123456789012345678901212345 bonds is less than eighty percent as England’s monarchs, is an apt case 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 volatile as that of the overall stock because we all think we “ know” what he 123456789012345678901234567890121234567890123456789012345678901212345 66 market. 123456789012345678901234567890121234567890123456789012345678901212345 was like. In his play R ichard III, Shakes- 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Volatility is less than eighty percent 6 123456789012345678901234567890121234567890123456789012345678901212345 peare provided a portrait of a monster of 6 (10) 123456789012345678901234567890121234567890123456789012345678901212345 for a balanced portfolio of stocks and 6 123456789012345678901234567890121234567890123456789012345678901212345 a man, twisted in both body and soul. 6 123456789012345678901234567890121234567890123456789012345678901212345 bonds compared to the overall stock 6 123456789012345678901234567890121234567890123456789012345678901212345 Shakespeare’s great artistry and vivid 6 123456789012345678901234567890121234567890123456789012345678901212345 market. 6 123456789012345678901234567890121234567890123456789012345678901212345 depiction of Richard has made us accept 6 123456789012345678901234567890121234567890123456789012345678901212345 E. The volatility of a balanced portfolio 6 123456789012345678901234567890121234567890123456789012345678901212345 this creature for the man. We are 6 123456789012345678901234567890121234567890123456789012345678901212345 of stocks and bonds is less than eighty 6 123456789012345678901234567890121234567890123456789012345678901212345 prepared, therefore, to interpret all the (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 percent of the overall stock market. 6 123456789012345678901234567890121234567890123456789012345678901212345 events around him in such a way as to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 justify our opinion of him. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 We accept that Richard executed his 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 brother Clarence, even though the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 records of the time show that Richard (20) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 pleaded for his brother’s life. We assume 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 that Richard supervised the death of King 6 6 123456789012345678901234567890121234567890123456789012345678901212345 H enry VI, overlooking that there is no 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 proof that H enry was actually murdered. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 And we recoil at Richard’s murdering his 6 (25) 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 two nephews, children of his brother’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 wife Elizabeth; yet we forget that 6 1 6 526 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 16. The author of the passage refers to Elizabeth had spent her time on the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Shakespeare’s “ great artistry and vivid throne plotting to replace her husband’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 depiction of Richard” (lines 10-11) most family in power with her own family. (30) 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 probably in order to O nce we appreciate the historical 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 context, especially the actions of Rich3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. make the point that studying R ichard 6 123456789012345678901234567890121234567890123456789012345678901212345 ard’s opponents, we no longer see his 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 III is the best way to understand 3456789012345678901234567890121234567890123456789012345678901212345 6 12 actions as monstrous. Richard becomes, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Richard as an historical figure. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 if not lovable, at least understandable. (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. explain why R ichard III is widely 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 What’s more, when we account for the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 acclaimed as one of Shakespeare’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tone of the times during which Richard 3456789012345678901234567890121234567890123456789012345678901212345 6 12 greatest works. 6 123456789012345678901234567890121234567890123456789012345678901212345 lived, as illuminated in literary works of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. contrast Shakespeare’s depiction of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that era such as M achiavelli’s T he Prince, 3456789012345678901234567890121234567890123456789012345678901212345 12 Richard with how Richard might have 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Richard’s actions seem to us all the more (40) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 described himself. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonable. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. illustrate how historians might 6 123456789012345678901234567890121234567890123456789012345678901212345 become prejudiced in their view of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 15. With which of the following statements historical figures. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 would the author of the passage most E. point out that historians should never 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 likely agree? rely on fictional works to understand 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and interpret historical events. 6 123456789012345678901234567890121234567890123456789012345678901212345 A. In R ichard III, Shakespeare portrays 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the king as more noble than he 6 123456789012345678901234567890121234567890123456789012345678901212345 17. It can be inferred from the passage 6 123456789012345678901234567890121234567890123456789012345678901212345 actually was. 6 123456789012345678901234567890121234567890123456789012345678901212345 information that M achiavelli’s T he Prince 6 123456789012345678901234567890121234567890123456789012345678901212345 B. The deeds of Elizabeth were even 6 123456789012345678901234567890121234567890123456789012345678901212345 helps show 6 123456789012345678901234567890121234567890123456789012345678901212345 more evil than those of Richard III. 123456789012345678901234567890121234567890123456789012345678901212345 66 A. that, in his play R ichard III, ShakesC. Richard III may have been innocent of 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 peare’s depictions of the king was some of the crimes that Shakespeare 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 historically accurate. leads us to believe he committed. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. that Richard’s actions were an D. Richard III may have had a justifiable 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 accurate reflection of the times in reason for killing H enry VI. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 which he lived. E. Shakespeare was unaware of many of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. that different authors often depict the the historical facts about the life of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 same historical figures in very Richard III. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 different ways. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. that M achiavelli was a more astute 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 than Shakespeare as an observer of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 human nature. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. that Richard’s actions as a king are 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 not surprising in light of his earlier 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 actions as a prince. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 527

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 19. City official: In order to revitalize our 18. PharmaCorp, which manufactures the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 city’s downtown business district, we drug Aidistan, claims that Aidistan is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 should increase the number of police more effective than the drug Betatol in 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 officers that patrol the district during treating Puma Syndrome. To support its 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 business hours. Three years ago, the city claim, PharmaCorp cites the fact that one 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 reduced the total size of its police force by 6 of every two victims of Puma Syndrome is 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 nearly 20 percent. Since then, retail treated successfully with Aidistan alone, as 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 businesses in the district have experienced 6 opposed to one out of every three treated 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 a steady decline in revenue. with Betatol alone. H owever, Pharma3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Corp’s claim cannot be taken seriously in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Any of the following, if true, would be an 6 123456789012345678901234567890121234567890123456789012345678901212345 light of the fact that the presence of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 effective criticism of the city official’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Gregg’s Syndrome has been known to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 recommendation EXCEPT: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 render Puma Syndrome more resistant to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Two years ago, the city established 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 any treatment. 6 123456789012345678901234567890121234567890123456789012345678901212345 more rigorous standards for the 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if true, would 6 123456789012345678901234567890121234567890123456789012345678901212345 retention and hiring of its police 6 123456789012345678901234567890121234567890123456789012345678901212345 most support the allegation that Pharma6 123456789012345678901234567890121234567890123456789012345678901212345 officers. 6 123456789012345678901234567890121234567890123456789012345678901212345 Corp’s claim cannot be taken seriously? 6 123456789012345678901234567890121234567890123456789012345678901212345 B. N ew businesses offering products or 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 services similar to those in the district 6 A. Among people who suffer from both 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 have emerged outside the district Puma Syndrome and Gregg’s Syn6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 recently. drome, fewer are treated with 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. The number of people who reside in Aidistan than with Betatol. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the district has not changed signifiB. Among people who suffer from both 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 cantly over the last three years. Puma Syndrome and Gregg’s Syn6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Businesses operating in the city but drome, fewer are treated with Betatol 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 outside the district have experienced than with Aidistan. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 declining revenues during the last C. Gregg’s Syndrome reduces Aidistan’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 three years. effectiveness in treating Puma 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. Some of the city’s police officers Syndrome more than Betatol’s 6 123456789012345678901234567890121234567890123456789012345678901212345 patrol areas outside as well as inside effectiveness in treating the same 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the district. syndrome. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Betatol is less effective than Aidistan 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 in treating Gregg’s Syndrome. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. N either Aidistan nor Betatol is 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 effective in treating Gregg’s Syn6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 drome. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 528 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 21. Since City X reduced the frequency with 20. Which of the following provides the most 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 which its service vehicles pick up recylogical completion of the passage below? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 clable materials from residences for 6 123456789012345678901234567890121234567890123456789012345678901212345 M ore and more consumers are being 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 transport to its recycling center, the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 attracted to sport utility vehicles because 3456789012345678901234567890121234567890123456789012345678901212345 6 12 volume of material that its service vehicles 3456789012345678901234567890121234567890123456789012345678901212345 6 12 they are safer to drive than regular cars, 6 123456789012345678901234567890121234567890123456789012345678901212345 transport to landfills for permanent 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 and because of the feeling of power a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 disposal has increased to unmanageable 3456789012345678901234567890121234567890123456789012345678901212345 6 12 person experiences when driving a sport 3456789012345678901234567890121234567890123456789012345678901212345 6 12 levels. H owever, the city cannot increase 6 123456789012345678901234567890121234567890123456789012345678901212345 utility vehicle. In its current advertising 2 3456789012345678901234567890121234567890123456789012345678901212345 1 the frequency of either its trash pickup or 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 campaign, Jupiter Auto Company empha3456789012345678901234567890121234567890123456789012345678901212345 6 12 its recycling pickup at city residences. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 sizes the low price of its new sport utility 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Based only the information above, which vehicle compared to the price of other 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 such vehicles. H owever, this marketing of the following strategies seems most 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 strategy is unwise because __________. appropriate for City X in the interest of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 reducing the volume of material that the A. Jupiter’s sport utility vehicle is not as 3456789012345678901234567890121234567890123456789012345678901212345 6 12 city’s service vehicles transport to land3456789012345678901234567890121234567890123456789012345678901212345 6 12 safe as those produced by competing 3456789012345678901234567890121234567890123456789012345678901212345 6 12 fills? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 automobile manufacturers. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. If Jupiter reduces the price of its sport A. Provide larger recycling containers to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 utility vehicle even further, Jupiter the residents of the city 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 would sell even more of these vehicles. B. Establish a community program to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. the retail price of Jupiter’s most increase awareness of the benefits of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 expensive luxury car is less than that recycling 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Establish additional recycling centers of its new sport utility vehicle. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 as near as possible to the city’s D. most consumers who purchase sport 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 residential areas utility vehicles are also concerned 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. Provide incentives to the city’s about the reliability of their vehicle. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 residents to reuse, rather than discard 6 E. consumers who purchase sport utility 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for pickup by the city’s service vehicles associate affordability with 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 vehicles, whatever they can lack of safety. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Ease restrictions on the types of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 materials the city’s service vehicles 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 will pick up for transport to its 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 recycling center 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 529

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 22. The pesticide Azocide, introduced to 25. N o nation in the world has experienced as 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 central valley farms three summers ago, significant a decline in its Yucaipa tree 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 has proven ineffective because other population as our nation. Yet only our 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 nation imposes a law prohibiting the use pesticides’ chemical compositions already 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of Yucaipa tree-bark oil in cosmetics. The in wide use neutralizing its desired effect. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 purpose of this law in the first place was 6 123456789012345678901234567890121234567890123456789012345678901212345 A. because other pesticides’ chemical 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to help maintain the Yucaipa tree popula3456789012345678901234567890121234567890123456789012345678901212345 6 12 compositions already in wide use 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tion, at least in this nation. But the law is 6 123456789012345678901234567890121234567890123456789012345678901212345 B. because of the chemical compositions 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 clearly unnecessary and therefore should 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of the pesticides already in wide use 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be repealed. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. due to other pesticides already in wide 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Which of the following, if true, would use, whose chemical compositions 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most seriously weaken the conclusion have been 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 drawn in the passage? D. since, due to the chemical composi3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tions of other pesticides already in A. This nation contains more Yucaipa 3456789012345678901234567890121234567890123456789012345678901212345 6 12 use, those pesticides have been 3456789012345678901234567890121234567890123456789012345678901212345 6 12 trees than any other nation. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. because of other pesticides and their 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Yucaipa tree-bark oil is not used for 6 123456789012345678901234567890121234567890123456789012345678901212345 chemical compositions already in use, 6 123456789012345678901234567890121234567890123456789012345678901212345 any consumer goods other than 6 123456789012345678901234567890121234567890123456789012345678901212345 which have been 6 123456789012345678901234567890121234567890123456789012345678901212345 cosmetics. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. The demand for cosmetics containing 6 123456789012345678901234567890121234567890123456789012345678901212345 23. To relieve anxiety, moderate exercise can 6 123456789012345678901234567890121234567890123456789012345678901212345 Yucaipa tree-bark oil is expected to 6 123456789012345678901234567890121234567890123456789012345678901212345 be equally effective as, and less addictive 6 123456789012345678901234567890121234567890123456789012345678901212345 decline in the future in other nations 6 123456789012345678901234567890121234567890123456789012345678901212345 than, most sedatives. 6 123456789012345678901234567890121234567890123456789012345678901212345 while continuing unabated in this 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. effective as, and nation. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 B. as effective as, while being 123456789012345678901234567890121234567890123456789012345678901212345 D. In other countries, labor used to 6 123456789012345678901234567890121234567890123456789012345678901212345 C. effectively equal to, but 123456789012345678901234567890121234567890123456789012345678901212345 harvest Yucaipa trees for cosmetics is 6 6 123456789012345678901234567890121234567890123456789012345678901212345 D. as effective as, and 123456789012345678901234567890121234567890123456789012345678901212345 less expensive than comparable labor 6 6 123456789012345678901234567890121234567890123456789012345678901212345 E. effective, and 6 123456789012345678901234567890121234567890123456789012345678901212345 in this nation. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. In this nation, some wild animals eat 6 123456789012345678901234567890121234567890123456789012345678901212345 24. The government’s means of disposal of Yucaipa tree bark, thereby contribut- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 war surplus following World War II met ing to their destruction. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 with vociferous objections by industrial123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ists, prominent advisors, and many others. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. of disposal of 6 123456789012345678901234567890121234567890123456789012345678901212345 B. in disposing 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. for the disposition of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. used in disposing 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. of disposing 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 530 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 27. The time it takes for a star to change its 26. Some official Web sites of regionally 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 brightness is directly related to the accredited colleges have received the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 highest possible rating from the Federal luminosity of it. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Department of Education. H owever, all 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. the luminosity of it 3456789012345678901234567890121234567890123456789012345678901212345 6 12 official Web sites of nationally accredited 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. the luminosity of its brightness 6 123456789012345678901234567890121234567890123456789012345678901212345 colleges have received the highest possible 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. the luminosity of a star 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rating from the same department. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. luminosity of it 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if added to the E. its luminosity 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 statements above, would provide most 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 support for the conclusion that all Web Questions 28–30 are based on the following 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 sites administered by individuals holding passage: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 advanced degrees in educational technol3456789012345678901234567890121234567890123456789012345678901212345 6 12 Line Diseases associated with aging in women 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ogy have received the highest possible 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 are difficult to correlate explicitly with 6 123456789012345678901234567890121234567890123456789012345678901212345 rating from the Federal Department of 6 123456789012345678901234567890121234567890123456789012345678901212345 estrogen deficiency because aging and Education? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 genetics are important influences in the 6 123456789012345678901234567890121234567890123456789012345678901212345 A. O nly official Web sites of nationally 6 123456789012345678901234567890121234567890123456789012345678901212345 development of such diseases. A number (5) 6 123456789012345678901234567890121234567890123456789012345678901212345 accredited colleges are administered 6 123456789012345678901234567890121234567890123456789012345678901212345 of studies, however, indicate a profound 6 123456789012345678901234567890121234567890123456789012345678901212345 by individuals holding advanced 123456789012345678901234567890121234567890123456789012345678901212345 effect of estrogen deficiency in syndromes 6 6 123456789012345678901234567890121234567890123456789012345678901212345 degrees in educational technology. 123456789012345678901234567890121234567890123456789012345678901212345 such as cardiovascular disease (including 6 6 123456789012345678901234567890121234567890123456789012345678901212345 B. All official Web sites of nationally 6 123456789012345678901234567890121234567890123456789012345678901212345 atherosclerosis and stroke) and os6 123456789012345678901234567890121234567890123456789012345678901212345 accredited colleges are administered 6 123456789012345678901234567890121234567890123456789012345678901212345 teoporosis—the loss and increasing (10) 6 123456789012345678901234567890121234567890123456789012345678901212345 by individuals holding advanced fragility of bone in aging individuals. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 degrees in educational technology. The amount of bone in the elderly 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. O nly Web sites that have not received skeleton—a key determinant in its 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the highest possible rating from the susceptibility to fractures—is believed to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Federal Department of Education are be a function of two major factors. The (15) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 administered by individuals not first is the peak amount of bone mass 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 holding advanced degrees in educaattained, determined to a large extent by 6 123456789012345678901234567890121234567890123456789012345678901212345 tional technology. 123456789012345678901234567890121234567890123456789012345678901212345 genetic inheritance. The marked effect of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 D. All official Web sites of nationally 6 123456789012345678901234567890121234567890123456789012345678901212345 gender is obvious—elderly men experi6 123456789012345678901234567890121234567890123456789012345678901212345 accredited colleges are administered 123456789012345678901234567890121234567890123456789012345678901212345 ence only one-half as many hip fractures 6 (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 by individuals holding advanced 6 123456789012345678901234567890121234567890123456789012345678901212345 per capita as elderly women. H owever, 6 123456789012345678901234567890121234567890123456789012345678901212345 degrees in educational technology. 6 123456789012345678901234567890121234567890123456789012345678901212345 African-American women have a lower 6 123456789012345678901234567890121234567890123456789012345678901212345 E. N o Web site administered by indi6 123456789012345678901234567890121234567890123456789012345678901212345 incidence of osteoporotic fractures than 6 123456789012345678901234567890121234567890123456789012345678901212345 viduals holding advanced degrees in 6 123456789012345678901234567890121234567890123456789012345678901212345 Caucasian women. O ther important 6 123456789012345678901234567890121234567890123456789012345678901212345 educational technology is an official 6 123456789012345678901234567890121234567890123456789012345678901212345 variables include diet, exposure to (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 Web site of a regionally accredited 6 123456789012345678901234567890121234567890123456789012345678901212345 sunlight, and physical activity. The 6 123456789012345678901234567890121234567890123456789012345678901212345 college. second major factor is the rate of bone 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 loss after peak bone mass has been 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 attained. While many of the variables 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that affect peak bone mass also affect (30) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 rates of bone loss, additional factors 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 531

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 30. It can be inferred from the passage that influencing bone loss include physiologi6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the peak amount of bone mass in women 6 cal stresses such as pregnancy and 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 lactation. It is hormonal status, however, 6 123456789012345678901234567890121234567890123456789012345678901212345 A. is not affected by either pregnancy or 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 (35) reflected primarily by estrogen and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 lactation. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 progesterone levels, that may exert the B. is determined primarily by diet. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 C. depends partly upon hormonal status. greatest effect on rates of decline in 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. may play a role in determining the skeletal mass. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rate of decrease in estrogen and 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 progesterone levels. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 28. Based upon the passage, which of the E. is not dependent upon genetic makeup. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 following is LEAST clearly a factor 12 6 123456789012345678901234567890121234567890123456789012345678901212345 affecting the rate of decline in bone mass? 2 3456789012345678901234567890121234567890123456789012345678901212345 1 31. Vining University’s teacher credential pro- 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 gram should be credited for the high grade- 6 3456789012345678901234567890121234567890123456789012345678901212345 12 A. Gender 3456789012345678901234567890121234567890123456789012345678901212345 6 12 point averages of high school students who 6 3456789012345678901234567890121234567890123456789012345678901212345 12 B. Exposure to sunlight 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 enroll in classes taught by Vining graduates. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Progesterone levels 6 123456789012345678901234567890121234567890123456789012345678901212345 M ore new graduates of Vining’s credential 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Age 6 123456789012345678901234567890121234567890123456789012345678901212345 program accept entry-level positions at 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Estrogen levels 6 123456789012345678901234567890121234567890123456789012345678901212345 Franklin H igh School than at any other high 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 school. And during the most recent aca6 123456789012345678901234567890121234567890123456789012345678901212345 29. In discussing the “ marked effect of 123456789012345678901234567890121234567890123456789012345678901212345 demic year, just prior to which many of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 gender” (lines 18–19), the author assumes Franklin’s teachers transferred to Valley View 6 123456789012345678901234567890121234567890123456789012345678901212345 all of the following EXCEPT 6 123456789012345678901234567890121234567890123456789012345678901212345 H igh School, the median grade point aver- 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 age of the students at Franklin has declined 6 A. the difference in incidence of hip 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 while at Franklin it has increased. fractures is not due instead to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 different rates of bone loss. 123456789012345678901234567890121234567890123456789012345678901212345 The argument above depends on which of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 B. the incidence of hip fractures among 6 123456789012345678901234567890121234567890123456789012345678901212345 the following assumptions? 6 123456789012345678901234567890121234567890123456789012345678901212345 elderly men as compared to elderly 6 123456789012345678901234567890121234567890123456789012345678901212345 A. The two high schools employ differing 6 123456789012345678901234567890121234567890123456789012345678901212345 women is representative of the total 6 123456789012345678901234567890121234567890123456789012345678901212345 methods of computing student grade 6 123456789012345678901234567890121234567890123456789012345678901212345 number of bone fractures among 6 123456789012345678901234567890121234567890123456789012345678901212345 point averages. 6 123456789012345678901234567890121234567890123456789012345678901212345 elderly men as compared to elderly B. N either high school has a peer tutoring 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 women. program that would afford the school 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 C. elderly women are not more accidentan advantage over the other in terms of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prone than elderly men. student academic performance. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 D. the population upon which the cited C. Just prior to last year, more teachers 6 6 123456789012345678901234567890121234567890123456789012345678901212345 transferred from Franklin to Valley View 6 123456789012345678901234567890121234567890123456789012345678901212345 statistic is based includes both 6 123456789012345678901234567890121234567890123456789012345678901212345 than from Valley View to Franklin. African-Americans and Caucasians. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The teachers who transferred from E. men achieve peak bone mass at the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Franklin to Valley View were replaced same age as women. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 with teachers who are also graduates 6 123456789012345678901234567890121234567890123456789012345678901212345 of Vining University’s teacher 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 credential program. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. The teachers who transferred from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Franklin to Valley View last year were 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 graduates of Vining’s teacher creden6 123456789012345678901234567890121234567890123456789012345678901212345 tial program. 6 1 6 532 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 33. While few truly great artists consider 32. M ore airplane accidents are caused by 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pilot error than any other single factor. themselves visionary, many lesser talents 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 The military recently stopped requiring its boast about their own destiny to lead the 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 pilots to obtain immunization shots way to higher artistic ground. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 against chemical warfare agents. These 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. While few truly great artists consider 6 123456789012345678901234567890121234567890123456789012345678901212345 shots are known to cause unpredictable 2 3456789012345678901234567890121234567890123456789012345678901212345 1 themselves visionary, many lesser tal- 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 dizzy spells which can result in pilot error. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ents boast about their own destiny to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Since many military pilots also pilot 6 123456789012345678901234567890121234567890123456789012345678901212345 lead the way to higher artistic ground. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 commercial passenger airliners, the reason 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. While many lesser talents boast about 3456789012345678901234567890121234567890123456789012345678901212345 6 12 for the military’s decision must have been 3456789012345678901234567890121234567890123456789012345678901212345 6 12 their own destinies to lead the way to 6 123456789012345678901234567890121234567890123456789012345678901212345 to reduce the number of commercial 2 3456789012345678901234567890121234567890123456789012345678901212345 1 higher ground, few truly great artists 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 airline accidents. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 consider themselves as visionary. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Which of the following, if true, provides C. M any lesser talents boast about their 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 most support for the conclusion drawn own destiny to lead the way to higher 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 above? artistic ground while few truly great 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 artists consider themselves as being 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Recently, more pilots have been 6 123456789012345678901234567890121234567890123456789012345678901212345 visionary. 6 123456789012345678901234567890121234567890123456789012345678901212345 volunteering for the immunization 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Few truly great artists consider 6 123456789012345678901234567890121234567890123456789012345678901212345 shots. 6 123456789012345678901234567890121234567890123456789012345678901212345 himself or herself a visionary while 6 123456789012345678901234567890121234567890123456789012345678901212345 B. All commercial airline flights are 6 123456789012345678901234567890121234567890123456789012345678901212345 many lesser talents boast about their 6 123456789012345678901234567890121234567890123456789012345678901212345 piloted by two co-pilots, whereas 6 123456789012345678901234567890121234567890123456789012345678901212345 own destinies to lead the way to 6 123456789012345678901234567890121234567890123456789012345678901212345 military flights are usually piloted by 6 123456789012345678901234567890121234567890123456789012345678901212345 higher artistic ground. only one. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. While many lesser talents boast about C. Chemical warfare is likely to escalate 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 their own destiny, few truly great in the future. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 artists consider themselves visionary, D. M ilitary pilots are choosing to resign 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to lead the way to higher artistic rather than obtain the immunization 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ground. shots. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. Recently, the number of military pilots 6 123456789012345678901234567890121234567890123456789012345678901212345 34. H istory shows that while simultaneously 6 123456789012345678901234567890121234567890123456789012345678901212345 also piloting commercial airliners has 6 123456789012345678901234567890121234567890123456789012345678901212345 attaining global or even regional domideclined. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 nance, a country generally succumbs to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 erosion of its social infrastructure. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. H istory shows that while simulta6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 neously attaining 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. H istory would show that, while 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 attaining 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. H istory bears out that, in the course 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of attaining 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. During the course of history, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 attainment of 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Throughout history, during any 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 country’s attaining 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 533

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 35. Connie: This season, new episodes of my either gradually or rapidly. Under the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 favorite television program are even more (5) gradual approach, a state bureau would 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 entertaining than previous episodes; so the decide if and when an enterprise is 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 program should be even more popular this prepared for privatization and which 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 season than last season. form is most suitable for it. H owever, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 gradual privatization would only prolong 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Karl: I disagree. After all, we both know that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (10) the core problems of inefficiency and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the chief aim of television networks is to maxi3456789012345678901234567890121234567890123456789012345678901212345 6 12 misallocation of both labor and capital. 6 123456789012345678901234567890121234567890123456789012345678901212345 mize advertising revenue by increasing the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Under one of two approaches to rapid 3456789012345678901234567890121234567890123456789012345678901212345 6 12 popularity of their programs. But this season 3456789012345678901234567890121234567890123456789012345678901212345 6 12 privatization, shares of an enterprise 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the television networks that compete with the 6 123456789012345678901234567890121234567890123456789012345678901212345 would be distributed among the enter2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 one that shows your favorite program are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 prise’s employees so that the employees (15) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 showing reruns of old programs during the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 would become the owners of the enter3456789012345678901234567890121234567890123456789012345678901212345 6 12 same time slot as your favorite program. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prise. This socialist-reform approach 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if true, would 6 123456789012345678901234567890121234567890123456789012345678901212345 discriminates in favor of workers who 6 123456789012345678901234567890121234567890123456789012345678901212345 provide the most support for Karl’s 123456789012345678901234567890121234567890123456789012345678901212345 happen to be employed by a modern and 6 6 123456789012345678901234567890121234567890123456789012345678901212345 response to Connie’s argument? 6 123456789012345678901234567890121234567890123456789012345678901212345 efficient enterprise as well as by placing (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 workers’ property at great risk by 6 123456789012345678901234567890121234567890123456789012345678901212345 A. What Connie considers entertaining does 6 123456789012345678901234567890121234567890123456789012345678901212345 requiring them to invest their property in 6 123456789012345678901234567890121234567890123456789012345678901212345 not necessarily coincide with what most 6 123456789012345678901234567890121234567890123456789012345678901212345 the same enterprise in which they are 6 123456789012345678901234567890121234567890123456789012345678901212345 television viewers consider entertaining. 6 123456789012345678901234567890121234567890123456789012345678901212345 employed rather than permitting them to 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Entertaining television shows are not 6 123456789012345678901234567890121234567890123456789012345678901212345 diversify their investments. (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 necessarily popular as well. 6 123456789012345678901234567890121234567890123456789012345678901212345 A better approach involves distribu6 123456789012345678901234567890121234567890123456789012345678901212345 C. Television networks generally 6 123456789012345678901234567890121234567890123456789012345678901212345 tion of shares in enterprises, free of 6 123456789012345678901234567890121234567890123456789012345678901212345 schedule their most popular shows 6 123456789012345678901234567890121234567890123456789012345678901212345 charge, among all the people by means of 6 123456789012345678901234567890121234567890123456789012345678901212345 during the same time slots as their 6 123456789012345678901234567890121234567890123456789012345678901212345 vouchers—a kind of investment money. 6 123456789012345678901234567890121234567890123456789012345678901212345 competitors’ most popular shows. 123456789012345678901234567890121234567890123456789012345678901212345 Some critics charge that voucher holders 6 (30) D. Certain educational programs which 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 would not be interested in how their are not generally considered entertain6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 enterprises are managed, as may be true ing are nevertheless among the most 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of small corporate shareholders in popular programs. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 capitalist countries who pay little E. The most common reason for a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 attention to their investments until the (35) network to rerun a television program 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 corporation’s profits fail to meet expecta- 6 is that a great number of television 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 tions, at which time these shareholders viewers request the rerun. 6 123456789012345678901234567890121234567890123456789012345678901212345 rush to sell their securities. While the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 resulting fall in stock prices can cause 6 123456789012345678901234567890121234567890123456789012345678901212345 6 Questions 36–39 are based on the following 123456789012345678901234567890121234567890123456789012345678901212345 serious problems for a corporation, it is (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 passage: 6 123456789012345678901234567890121234567890123456789012345678901212345 this very pressure that drives private 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 firms toward efficiency and profitability. (T he follow ing passage w as w ritten in 1991.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 O ther detractors predict that most people 6 123456789012345678901234567890121234567890123456789012345678901212345 Line O ne of the cornerstones of economic 6 123456789012345678901234567890121234567890123456789012345678901212345 will sell their vouchers to foreign 6 123456789012345678901234567890121234567890123456789012345678901212345 reform in the formerly Communist states 6 123456789012345678901234567890121234567890123456789012345678901212345 capitalists. These skeptics ignore the (45) 6 123456789012345678901234567890121234567890123456789012345678901212345 is privatization, which can be approached 6 123456789012345678901234567890121234567890123456789012345678901212345 capacity of individuals to consider their 6 1 6 534 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 2 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 own future—that is, to compare the 36. Which of the following is N O T mentioned 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 future flow of income secured by a in the passage as a possible adverse 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 voucher to the benefits of immediate consequence of rapid privatization? 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 (50) consumption. Even if an individual should 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Undue prolongation of inefficiency 3456789012345678901234567890121234567890123456789012345678901212345 6 12 decide to sell, the aim of voucher privati3456789012345678901234567890121234567890123456789012345678901212345 6 12 and misallocation 6 123456789012345678901234567890121234567890123456789012345678901212345 zation is not to secure equality of property 2 3456789012345678901234567890121234567890123456789012345678901212345 1 B. Loss of ownership in domestic private 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 but rather equality of opportunity. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 enterprises to foreign concerns 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 C. Financial devastation for employees of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 38. In responding to those “ skeptics” who private enterprises 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 claim that people will sell their vouchers 12 D. Inequitable distribution of wealth 6 123456789012345678901234567890121234567890123456789012345678901212345 to foreign capitalists (lines 43–45), the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 among employees of various enter3456789012345678901234567890121234567890123456789012345678901212345 6 12 author implies that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 prises 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. Instability in stock prices A. foreign capitalists will not be willing 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to pay a fair price for the vouchers. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 39. Which of the following is LEAST accurate 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. the future flow of income is likely in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in characterizing the author’s method of many cases to exceed the present 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 argumentation in discussing the signifiexchange value of a voucher. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 cance of falling stock prices (lines 38–42)? C. foreign investment in a nation’s 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 enterprises may adversely affect 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Describing a paradox that supports 6 123456789012345678901234567890121234567890123456789012345678901212345 currency exchange rates. 6 123456789012345678901234567890121234567890123456789012345678901212345 the author’s position 6 123456789012345678901234567890121234567890123456789012345678901212345 D. although the skeptics are correct, their 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Asserting that one drawback of an 6 123456789012345678901234567890121234567890123456789012345678901212345 point is irrelevant in evaluating the 6 123456789012345678901234567890121234567890123456789012345678901212345 approach is outweighed by counter6 123456789012345678901234567890121234567890123456789012345678901212345 merits of voucher privatization. 6 123456789012345678901234567890121234567890123456789012345678901212345 vailing considerations E. foreign capitalists are less interested in 123456789012345678901234567890121234567890123456789012345678901212345 66 C. Rebutting an opposing position by 123456789012345678901234567890121234567890123456789012345678901212345 the success of voucher privatization 6 123456789012345678901234567890121234567890123456789012345678901212345 suggesting an alternative explanation 6 123456789012345678901234567890121234567890123456789012345678901212345 than in making a profit. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Discrediting an opposing argument by 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 questioning its relevance 6 123456789012345678901234567890121234567890123456789012345678901212345 37. Which of the following would the author 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Characterizing an argument against a 6 123456789012345678901234567890121234567890123456789012345678901212345 probably agree is the LEAST desirable 6 123456789012345678901234567890121234567890123456789012345678901212345 course of action instead as an 6 123456789012345678901234567890121234567890123456789012345678901212345 outcome of economic reform in formerly 6 123456789012345678901234567890121234567890123456789012345678901212345 argument in its favor 6 123456789012345678901234567890121234567890123456789012345678901212345 Communist countries? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. Effective allocation of labor 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Equitable distribution of property 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 among citizens 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Financial security of citizens 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. Equal opportunity for financial 6 123456789012345678901234567890121234567890123456789012345678901212345 success among citizens 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Financial security of private enterprises 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 535

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 41. H umans naturally crave to do good, act 40. Currently, the supply of office buildings in 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 reasonably, and to think decently, these this state far exceeds demand, while 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 demand for single-family housing far urges must have a global purpose in order 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 exceeds supply. As a result, real estate to have meaning. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 developers have curtailed office building 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. to think decently, these 6 123456789012345678901234567890121234567890123456789012345678901212345 construction until demand meets supply, 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. think decently, yet these 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and have stepped up construction of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. to decently think, and these 3456789012345678901234567890121234567890123456789012345678901212345 6 12 single-family housing. The state legislature 6 123456789012345678901234567890121234567890123456789012345678901212345 D. thinking decently, but these 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 recently enacted a law eliminating a state 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. think decent, these 3456789012345678901234567890121234567890123456789012345678901212345 6 12 income tax on corporations whose 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 primary place of business is this state. In 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 response, many large private employers 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 from other states have already begun to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 relocate to this state, and according to a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reliable study, this trend will continue 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 during the next five years. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following predictions is best 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 supported by the information above? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. During the next five years, fewer new 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 office buildings than single-family 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 houses will be constructed in the state. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Five years from now, the available 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 supply of single-family housing in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 state will exceed demand. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. Five years from now, the per capita 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 income of the state’s residents will 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 exceed current levels. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. During the next five years, the cost of 6 123456789012345678901234567890121234567890123456789012345678901212345 purchasing new single-family residen6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 tial housing will 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 decrease. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. During the next five years, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 number of state residents working at 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 home as opposed to working in office 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 buildings will decrease. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 536 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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Answers and Explanations See Appendix for score conversion tables to determine your score. Be sure to keep a tally of correct and incorrect answers for each test section.

1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Issue—Evaluation and Scoring 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Evaluate your Issue-Analysis essay on a scale of 1 to 6 (6 being the highest score) according to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the following five criteria: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 1. Does your essay develop a position on the issue through the use of incisive reasons and 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 persuasive examples? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Are your essay’s ideas conveyed clearly and articulately? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay maintain proper focus on the issue, and is it well organized? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure, vocabulary, and idiom? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument—Evaluation and Scoring 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Evaluate your Argument-Analysis essay on a scale of 1 to 6 (6 being the highest score) according 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to the following five criteria: 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. Does your essay identify the key features of the argument and analyze each one in a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 thoughtful manner? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Does your essay support each point of its critique with insightful reasons and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 examples? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay develop its ideas in a clear, organized manner, with appropriate 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 transitions to help connect ideas together? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure, vocabulary, and idiom? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The following series of questions, which serve to identify the Argument’s four distinct 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 problems, will help you evaluate your essay in terms of criteria 1 and 2. To earn a score of 4 or 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 537

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 higher, your essay should identify at least three of these problems and, for each one, provide at 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 least one example or counterexample that supports your critique. (Your examples need not be 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the same as the ones below.) Identifying and discussing all four problems would help earn you 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 an even higher score. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 • Does the Argument draw a questionable analogy between O ak City’s circumstances 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 and M apleton’s? (Perhaps the percentage of students needing off-campus housing, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 which might affect property values, is significantly greater in one town than the other.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 • Does the Argument draw a questionable analogy between four-year colleges and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 community colleges? (Perhaps a four-year college would bring greater prestige or higher 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 culture to the town.) 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 • Is the presence of M apleton’s new community college necessarily the actual cause of the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 decline in M apleton’s property values and rents? (Perhaps some other recent development 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is responsible instead.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 • Is it necessary to refuse the new college in order to prevent a decline in property values 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and rents? (Perhaps O ak City can counteract downward pressure on property values 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and rents through some means.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Quantitative Ability 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. E Since the answer choices are expressed in decimal terms, rewrite all three terms in the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 question to decimals, then add: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 =.49 5 .7 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 5 .75 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 80% 5 .8 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 .7 1 .75 1 .8 5 2.25 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4 16 123456789012345678901234567890121234567890123456789012345678901212345 2. D The amount of the decrease is $4. The percent of the decrease is , or , or 16% . 6 6 123456789012345678901234567890121234567890123456789012345678901212345 25 100 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3. E Statement (1) alone provides no information about how many students a bus can carry, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 so it is insufficient to answer the question. Statement (2) provides only an average. Some 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 buses might have a greater capacity, while others might have a lesser capacity. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. C To answer the question, you need to know drive B’s total capacity as well as the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 amount (number of gigabytes) of drive B’s capacity currently used. Statement (1), 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 together with the information given in the question stem, provides the former, while 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) provides the latter. [The storage capacities of drives A and B are 17 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 and 20, respectively. O f drive B’s 20 gigabyte capacity, 42.5% (8.5 gigabytes) is 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 currently used.] 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 538 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 5. E You could piece together the panes into either a single column (or row) of 8 panes or 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 into 2 adjacent columns (or rows) of 4 panes each. In the first case, the door’s 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 perimeter would be 18. In the second case, the door’s perimeter would be 12. Thus, 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 statement (1) alone is insufficient to answer the question. Statement (2) alone is 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 insufficient for the same reason. Both statements together still fail to provide 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 sufficient information to determine the shape (or perimeter) of the door. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 6. D O ne way to solve this problem is to substitute each answer choice in turn into the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 x 2 3456789012345678901234567890121234567890123456789012345678901212345 1 given fraction. You can also solve the problem algebraically. Let represent the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 original fraction. Add 4 to both the numerator and denominator, then cross-multiply 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 to solve for x : 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 x 14 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 5 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2x 1 4 8 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 8x 1 32 5 10x 1 20 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 12 5 2x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 65x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The original denominator is 2x , or 12. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 7. B Because the t-terms are the same (.2t), the quickest way to solve for s is with the 6 123456789012345678901234567890121234567890123456789012345678901212345 addition-subtraction method. M anipulate both equations so that corresponding 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 terms “ line up,” then add the two equations: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 .2t 1 .6s 5 2.2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 .2t 1 .5s 5 1.1 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1.1s 5 3.3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 s 5 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 8. C To determine the size of Unit C, first determine the size of Unit D as a percentage of 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the total warehouse size. Unit D occupies 15,500 square feet, or approximately 11% , 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 of the total 140,000 square feet in the warehouse. Thus, Unit C occupies 19% of that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 total (100% 2 28% 2 42% 2 11% 5 19% ). The question asks for the difference in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 size between Unit A (28% ) and Unit D (19% ). That difference is 9% of the 140,000 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 total square feet, or 12,600 square feet. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 9. D The size of Unit B is 42% of 140,000 square feet, or about 59,000 square feet. Thus, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the combined size of Unit B and Unit D is approximately 74,500 square feet. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 539

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 10. B O ne way to solve this problem is to substitute each answer choice, in turn, for 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Carrie’s current age. You can also solve the problem by setting up an algebraic 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 equation. Letting x equal Benjamin’s present age, you can express Benjamin’s age 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 eight years from now as x 1 8. Similarly, you can express Carrie’s present age as 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 (x 1 24), and her age eight years from now as (x 1 32). Set up the following equation 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 relating Carrie’s age and Benjamin’s age eight years from now: 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 x 1 32 5 2(x 1 8) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 x 1 32 5 2x 1 16 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 16 5 x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Benjamin’s current age is 16 and Carrie’s current age is 40. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 11. A Because of the two right angles indicated in the figure, A B i D C, and A BCD is a 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 trapezoid. The area of a trapezoid 5 h~b 1 b !, where h is the height and each b 6 1 2 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is a parallel base (side): 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 A 5 (9)(10 1 12) 5 99 6 123456789012345678901234567890121234567890123456789012345678901212345 2 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 12. C Simplify all four terms by removing perfect squares or cubes. Then, for each fraction, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 divide common factors: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3 3 6 123456789012345678901234567890121234567890123456789012345678901212345 81x 7 =162x 5 ~3x 2 !=3x ~9x 2 !=2x = 3 6 123456789012345678901234567890121234567890123456789012345678901212345 2 5 2 5 =3x 2 3 =2x 3 2 2 4 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3x 3x =9x =27x 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 13. B Since each of the two series is strictly arithmetic (all terms are evenly spaced), for 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 each series the mean is the same as the median: exactly midway between the least 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and greatest numbers. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 1 16 17 6 123456789012345678901234567890121234567890123456789012345678901212345 M ean of first series: 5 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 17 1 32 49 6 123456789012345678901234567890121234567890123456789012345678901212345 M ean of second series: 5 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 49 17 32 6 123456789012345678901234567890121234567890123456789012345678901212345 N ow, do the subtraction: 2 5 , or 16. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 2 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 14. E If unequal quantities (c and d) are added to unequal quantities of the same order 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (a and b), the result is an inequality of the same order. (E) essentially states this rule. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 540 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 15. D First, you need to determine the volume of the cylindrical tube. The tube’s radius (r) is 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 123456789012345678901234567890121234567890123456789012345678901212345 and its length is 4. Apply the formula for the volume of a right cylinder (V 5 pr2 h): 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ~4! 5 p ~4! 5 p V 5 p 6 123456789012345678901234567890121234567890123456789012345678901212345 2 4 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 The tube’s volume is p (approximately 3.1) cubic feet. Regardless of its shape, the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 tube will not fit into a box containing only 3 cubic feet. Thus, given statement (1) 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 alone, you can answer the question. (The answer is no.) Statement (2) alone allows 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 for an infinite variety of box shapes. H owever, no shape with a surface area of 14 will 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 accommodate the tube. H ow do you know this? Assume that the box’s dimensions 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are 3 3 1 31. It’s total surface area is exactly 14, yet it’s too short (only 3 feet long) 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to accommodate the tube, which is 4 feet long. Visualize altering the box’s shape 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (making it either “ fatter” or “ skinnier” ) while maintaining a surface area of 14. To 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 increase its length, you must sacrifice surface area of the base (and vice versa). In any 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 case, a box with surface area of 14 cannot accommodate the tube. Thus, statement 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) alone suffices to answer the question. (Again, the answer is no.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 16. C Using negative integers with the least absolute value yields the least product. Start 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 with 21, then decrease the values of x and y if necessary. The first two values that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 satisfy the equation are: y 5 22, x 5 21 [21 2 (22) 5 1]. Accordingly, x y 5 2. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 17. E N either statement (1) nor (2) alone provides any information about the number of 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 yellow jellybeans. Considering both statements together, however, we know that the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 jar must contain 7 or more black jellybeans (along with exactly 6 pink jellybeans). 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Accordingly, the jar can contain a maximum of 7 yellow jellybeans. If the jar contains 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 either 6 or 7 yellow jellybeans, the answer to the question is no. H owever, if the jar 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 contains 5 or fewer jellybeans, the answer to the question is yes. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 18. C The expression a 2 b can also be expressed in its factored form: (a 1 b)(a 2 b). 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 N otice the similarity between this form and the binomial expression given in the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 question. Factor out the constants (numbers) in the binomial so that it more closely 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 resembles the factored form of a 2 b : 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (3a 1 3b)(2a 2 2b) 5 6(a 1 b)(a 2 b) 5 6(a2 2 b 2 ) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 2 2 2 b greater than 6(a 2 b )? Considering statement So the question is asking: Is a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) alone, (a2 2 b 2 ) might be either positive or negative, depending on whether the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 absolute value of b is less than a or greater than a. Accordingly, (6)(a2 2 b 2 ) might be 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 either greater or less than (a2 2 b 2 ), and statement (1) alone does not suffice to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. Considering statement (2) alone, whether (a2 2 b 2 ) is positive or 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 negative depends on the value of b, and therefore (6)(a 2 b ) might be either greater 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 or less than (a 2 b ). Thus, statement (2) alone does not suffice to answer the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 question. H owever, both statements together do suffice to answer the question. Given 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 that b , a , 21, (a2 2 b 2 ) must be a negative number. M ultiplying this negative 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 541

SD

SD

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 number by 6 yields an even lesser number (to the left on the real number line). 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Therefore, 6(a2 2 b 2 ) , a2 2 b 2 . (The answer to the question is yes.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 19. E Apply the defined operation to 2100 and to 100 in turn, by substituting each value 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 for x in the operation: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 b 2100 c 5 298 2 (99) 2 (2101) 2 (2102) 5 298 1 99 1 101 1 102 5 204 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 b 100 c 5 102 2 101 2 99 2 98 5 2196 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Then combine the two results: 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 b 2100 c 2 b 100 c 5 204 2 (2196) 5 204 1 196 5 400 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 20. A Given statement (1) alone, DQ R S must be a 1:1:=2 triangle. Accordingly, Q R ≅ 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 SR . Since PQ R S is a rectangle, Q R and SR are congruent to their respective opposite 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 sides. Thus, all four sides are congruent, and PQ R S must be a square. Statement (2) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 alone provides no new information. We already know that PQ R S is a rectangle and, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 accordingly, that the length of PS is 12. PQ and SR could be any length, so the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rectangle might, but need not, be a square. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 21. D Consider statement (1) alone. If the dealer earned a 50% profit from the sale to the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 customer, determining the amount the customer paid is a simple matter of adding 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 50% of $10,000 to $10,000. Thus, statement (1) alone suffices to answer the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 question. Consider statement (2) alone. If the dealer’s cost was two thirds the amount 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 the customer paid, then the customer paid of dealer’s cost. Determining how much 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 the customer paid is a simple matter of multiplying $10,000 by . Thus, statement (2) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 alone suffices to answer the question. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 22. A Computing standard deviation involves these steps: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) Compute the arithmetic mean (simple average) of all terms in the set 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) Compute the difference between the mean and each term 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (3) Square each difference you computed in step (2) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (4) Compute the mean of the squares you computed in step (3) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (5) Compute the non-negative square root of the mean you computed in step (4) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Applying steps 1–4 to each of the five answer choices yields the following results: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5 8 7 8 14 6 123456789012345678901234567890121234567890123456789012345678901212345 ~B! ~C! ~D! ~E! ~A! 6 123456789012345678901234567890121234567890123456789012345678901212345 3 2 3 2 3 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Choice (A) is the only fraction that exceeds 4. [There’s no need to compute the square 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 roots of any of these fractions (step 5), since their relative values would remain the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 same.] 6 1 6 542 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 23. B In each set are three distinct member pairs. Thus the probability of selecting any pair 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 123456789012345678901234567890121234567890123456789012345678901212345 is one in three, or . Accordingly, the probability of selecting fruit and salad from the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 1 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 appetizer menu along with squash and peas from the vegetable menu is 3 5 . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 3 9 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 24. D Statement (1) says essentially: A 2 C . B. Given that bin A contains exactly twice as 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 many potatoes as bin B, you can substitute 2B for A in the inequality, then determine 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the relationship between the number of potatoes in bins B and C: 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A 2C.B 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2B 2 C . B 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B2C.0 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B.C 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Thus, statement (1) alone suffices to answer the question. (The answer is yes.) Given 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 statement (2) alone, C must be less than A . (If you’re not certain of this, use a few 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 simple numbers to confirm it.) Given that B5 A , you can conclude from statement 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) alone that B . C. Statement (2) alone also suffices to answer the question. (N otice 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 that you can answer the question with either statement alone without the additional 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 fact that bin A contains ex actly 11 more potatoes than bin C. This additional 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 information appears to make the problem more complicated than it really is.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 25. C The largest possible rectangular area is formed by a square, the area of which is the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 square of any side. (The length of each side is one-fourth the rope’s length.) The 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 largest possible triangular area is formed by an equilateral triangle, the area of which 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 is defined as follows (s 5 the length of any side): 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 s2 =3 6 123456789012345678901234567890121234567890123456789012345678901212345 A rea 5 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 O ne way to compare the two areas is to substitute a hypothetical value for the length 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 of the ropes. Assume the length of each rope before it was cut was 12. The length of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 each of the triangle’s sides is 4, while the length of the square’s sides is 3: 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 4 3 = 6 123456789012345678901234567890121234567890123456789012345678901212345 The triangle’s area 5 5 4 3 ' 4~1.7! ' 6.8 = 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 The square’s area 5 3 5 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The ratio of 6.8 to 9 is approximately 3 to 4. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 543

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 26. E Any multiple-digit prime number must end in an odd digit other than 5 (1, 3, 7, or 9). 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Considering statement (1) alone, Z must be either 1 or 3, and five possibilities emerge: 6 3456789012345678901234567890121234567890123456789012345678901212345 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 601 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 421 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 241 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 403 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 223 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) alone allows for many possibilities, since Z can be either 1, 3, 7 or 9. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Statements (1) and (2) together eliminate only three of the possibilities, leaving more 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 than one answer. 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 4 bc a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 27. A Given statement (1), a 5 d. Substituting a for d in the fraction: 3456789012345678901234567890121234567890123456789012345678901212345 12 , or simply bc. 6 4 3456789012345678901234567890121234567890123456789012345678901212345 6 12 a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Given that b and c are both positive but less than 1, bc , 1, and statement (1) alone 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 suffices to answer the question. (The answer to the question is yes.) H owever, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 statement (2) alone is insufficient to answer the question. Even if d is greater than 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 zero, statement (2) fails to provide sufficient information to determine the relative 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 values of the numerator and denominator. A sufficiently small d-value relative to the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 values of a, b, and c results in a quotient greater than 1, whereas a sufficiently greate 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 relative d-value results in a quotient less than 1. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 28. C 3x is a multiple of 3; thus, adding 5 to that number yields a number that is not a 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 multiple of 3. N one of the other choices fit the bill. (A) is incorrect because x . 0 and 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 therefore must equal 3 or some multiple of 3. (B), (D) and (E) are incorrect because 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 any integer multiplied by 3 is a multiple of 3, and any multiple of 3 (such as 6 or 18) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 added to a multiple of 3 is also a multiple of 3. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 29. D The number of dollars increases proportionately with the number of pieces of paper. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 The question is essentially asking: “ 1 is to m as what is to p?” First, set up a 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 proportion (equate two ratios, or fractions). Then convert pieces of paper to reams 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (divide m by 500) or reams to pieces (multiply p by 500). (The second conversion 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 method is used below.) Cross-multiply to solve for x : 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 x 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5 6 123456789012345678901234567890121234567890123456789012345678901212345 m 500p 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 m x 5 500p 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 500p 6 123456789012345678901234567890121234567890123456789012345678901212345 x5 6 123456789012345678901234567890121234567890123456789012345678901212345 m 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 544 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 30. D At the end of September the approximate share prices of the three companies’ stocks 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 were as follows: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Ardent stock: $16 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 BioFirm stock: $50 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 CompuWin stock: $34 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The aggregate price of Ardent stock and BioFirm stock was $66, which exceeds the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 price of CompuWin stock ($34) by approximately 100% . 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 31. B During August, the price of BioFirm stock and CompuWin stock increased by a 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 combined amount of about $5. During the same month the price of Ardent stock 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 decreased by about $6. The net aggregate change is nearly zero. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 32. D The key to this problem involves perpendicular lines and the concept of slope. The 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 1 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 slope of l1 is , which means that every 2 units from left to right (the line’s “ run” ) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 corresponds to 1 unit upward (vertically) on the plane (the line’s “ rise” ). Since the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 angle at point A is a right angle, the slope of A B must be 22 (a “ drop” or “ negative 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rise” of 2 units for every 1 unit from left to right). Drawing a plumb line down from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 point A reveals that, in order to attain these slopes, the height (altitude) of DO A B 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 must be 2: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The area of any triangle is defined as one-half the product of its base and height (alti- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 tude). Given a base (O B) of 5 and an altitude of 2, the area of DO A B must equal 5. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 33. B Considering statement (1) alone, it is possible that any number of the remaining 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 students, from 0 to 25, are enrolled in Algebra I. Statement (2) alone suffices to 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. Given that 12 students are enrolled in English Literature while 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 are enrolled in World H istory, if the total enrollment for all three classes is 35, then 14 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 students must be enrolled in Algebra I. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 545

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 34. D Given that twice as many student tickets as adult tickets were sold, two-thirds (18) of 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the 27 tickets sold were student tickets, while one-third (9) were adult tickets. You 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 can express the ticket sales revenue by way of the following equation (A 5 adult 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 ticket price, S 5 student ticket price): 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 9A 1 18S 5 $180 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Statement (1) provides the value of A , which allows you to determine the value of S 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (the answer to the question): 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 9~10! 1 18S 5 180 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 18S 5 90 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 S55 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Statement (2) allows you to substitute 2S for A in the equation above, thereby 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 allowing you to determine the value of S (the answer to the question): 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 9~2S! 1 18S 5 $180 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 36S 5 $180 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 S 5 $5 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 35. A The product of an even integer and any other integer is always even. Therefore, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 statement (1) alone establishes that ab and cd are both even and, accordingly, that ab 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 1 cd is even (the sum of two even integers is always even). Given statement (2) alone, 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 however, although ab must be even, cd might be either odd or even, depending on the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 value of c. Accordingly, ab 1 cd might be either odd or even, and statement (2) alone 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 does not suffice to answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 36. B The key to this problem is in determining the interior angles of the various triangles 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 formed by the runways. The interior angle formed by the 120° turn from runway 1 to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 2 is 60° (a 180° turn would reverse the airplane’s direction). Similarly, the interior 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 angle formed by the 135° turn from runway 1 to 3 is 45° (180° 2 135°). Two triangle 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 “ angle triplets” emerge: a 45°-45°-90° triplet and a 30°-60°-90° triplet, as shown in 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the next figure. Since the sum of the measures of any triangle’s interior angles is 180°, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the remaining angles can also be determined: 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The only angle measure listed among the answer choices that does not appear in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 figure above is 55°. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 546 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 37. E You can answer this question without knowing the total number of legislators who 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 voted, because the question involves ratios only. Think of the legislature as containing 6 3456789012345678901234567890121234567890123456789012345678901212345 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 5 3 8 123456789012345678901234567890121234567890123456789012345678901212345 8 voters divided into two parts: 1 5 . For every 5 votes in favor, 3 were cast 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 8 8 8 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 5 123456789012345678901234567890121234567890123456789012345678901212345 against the motion. Thus, 5 out of every 8 votes, or , were cast in favor of the motion. 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 8 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 12 1. E The original sentence (A) is faulty in two respects. First, the sentence treats the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 compound subject (interest rates and the supply of m oney) as singular by using either 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 . . . or; the predicate should agree by also referring to the subject in the singular form, 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 using a factor rather than factors. Second, the verb phrase can . . . be is improperly 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 split. Third, the phrase can . . . be factors contributing to is redundant and wordy. (E) 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 remedies all the original sentence problems by uniting the verb parts, rewording the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 predicate to agree in form with the subject, and removing the redundant language. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. D The original version is wordy and very awkward. (D) is clear and concise. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3. A The original version is perfectly fine. The phrase sim ilar to sets up a comparison 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 between soil composition on M ars and soil composition on Earth. The relative 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 pronoun that is proper here to refer to the latter. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 4. B The argument relies on the assumption that alcoholics die relatively young only 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 because alcoholism increases a person’s susceptibility to life-threatening diseases, and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 not for other reasons as well. (B) provides explicitly that those other possible reasons 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 were ruled out in compiling the insurance statistics cited in the report. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. C Statement (C) helps explain last year’s sales results by suggesting that sales of 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 products three years old and older could have fallen sharply during the year. Thus, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the proportion of sales produced by newer products could have grown, even without 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 popular new products. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6. E It can reasonably be inferred that the “ new conditions” which sparked the divergence 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 in pistol shrimp are an aspect of the two oceans’ “ distinctive personalities,” which the 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 author states began to emerge “ long before the isthmus was fully formed.” Statement 6 123456789012345678901234567890121234567890123456789012345678901212345 6 (E) contradicts the inference. 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 7. A The author discusses pistol shrimp as an example of twin species, or geminates. Thus, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 (A) expresses the author’s immediate purpose in mentioning the mating habits of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 pistol shrimp. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 8. C The second paragraph provides ample support for this inference. The author states 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 that the terrestrial species migrating south were “ better colonizers” than the ones 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 migrating north, that m ore than half of those in the south today came from the north, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 and that only three animal species migrating north across the isthmus survive today. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 It is readily inferable, then, that more than three species that migrated south across 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 the isthmus survive today. 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 547

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 9. D The original sentence (A) contains a vague pronoun reference. It is unclear as to what 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the second that refers. (D) restates the idea of the first clause of the original sentence 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 more succinctly and clearly, as well as making it clear by the use of the phrase, and 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 this fact, that the latter part of the sentence refers to the earlier part. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 10. B The conclusion of the argument is that the claim made by those who have 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 discontinued regular exercise is born of laziness; in other words, these people are 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 making this claim because they are lazy. O ne effective way to refute the argument is 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 to provide convincing evidence that directly contradicts the conclusion. (B) provides 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 just such evidence, by showing that these people are not in fact lazy. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 11. D The original argument’s line of reasoning is essentially as follows: 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Prem ise: The well-paid engineers at CompTech do not quit their jobs. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Conclusion: If M icroFirm engineers are not well-paid, they will quit their jobs. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 You can express this argument symbolically as follows: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: All A’s are B’s. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: If not A, then not B. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The reasoning is fallacious (flawed), because it fails to account for other possible 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 reasons why M icroFirm engineers have not left their jobs. (Some B’s might not be 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A’s.) (D) is the only answer choice that demonstrates the same essential pattern of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 flawed reasoning. To recognize the similarity, rephrase the argument’s sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure to match the essence of the original argument: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: All people who practice diligently (A) achieve perfection (B). 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: If one does not practice diligently (not A) one cannot achieve 6 123456789012345678901234567890121234567890123456789012345678901212345 perfection (not B). 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 12. B In the original version, the advent and from the tim e of are redundant. Also, since is 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 more appropriate than from to express the sentence’s intended meaning. (B) corrects 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 both problems. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 13. B The original sentence (A) is not a complete sentence. (B) completes the sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 without committing any errors in grammar or diction. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 14. A The original sentence (A) properly uses the correlative not only . . . but also. The two 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 modifying phrases (not only by increased and but also by increased) are 6 123456789012345678901234567890121234567890123456789012345678901212345 66 grammatically parallel. 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 15. C Shakespeare depicts Richard III as a monster with a twisted soul—a depiction that 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 leads us to believe that Richard could well have been responsible for the deaths of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 both his brother Clarence and H enry VI. H owever, the author of the passage tells us 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that there is historical evidence that Richard did not kill his brother, and that there is 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 no proof that H enry VI was actually murdered. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 1 6 548 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 16. D In the passage, the author first tells us that historians sometimes think they know an 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 historical figure better than they really do. Then the passage’s author explains how 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 this can happen by providing an illustrative example—a biographical work (R ichard 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 III) that is so compelling in its development of the main character that even an 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 historian can be unduly influenced by it. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 17. B According to passage, M achiavelli’s T he Prince provides information about the tone 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of the times in which Richard lived. The passage’s final sentence tells us that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 Richard’s actions seem “ reasonable” in light of the tone of the times—in other words, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that his actions reflected the times. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 18. A This argument relies on the assumption that Gregg’s Syndrome is more prevalent 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 12 among Puma Syndrome victims who take Betatol than among those who take 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Aidistan. (A) essentially affirms this assumption, although it expresses it in a 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 somewhat different way. Given that Gregg’s Syndrome renders any Puma Syndrome 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 treatment less effective, if victims who have both syndromes are treated with Betatol 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 while victims who have only Puma Syndrome are treated with Aidistan, then Aidistan 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 will appear to be more effective, although the absence of Gregg’s Syndrome might in 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fact be the key factor that explains the differing results. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 19. C In all likelihood, the district’s residents contribute to the revenues of businesses there 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 by purchasing goods and services from them. A net loss in the number of district 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 residents would provide an alternative explanation for the loss of revenue. (C) rules 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 out this possibility, thereby strengthening the claim that the loss in revenue was due to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the city’s reduction in its police force and, accordingly, that increasing the size of the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 force will reverse the decline in revenues. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 20. E The passage boils down to the following: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: People buy sport utility vehicles because they believe these vehicles are 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 safe. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: To sell a vehicle, a manufacturer should not emphasize affordability. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Choice (E) provides the assumption needed to render the argument logically 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 convincing: 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: People buy sport utility vehicles because they believe these vehicles are 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 safe. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise (E): People do not believe that affordable vehicles are safe. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: To sell a sport utility vehicle, a manufacturer should not emphasize 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 its affordability. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 21. D Regardless of the reason for the increase in the volume of material transported to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 landfills, reducing the volume of material available for transport to landfills would 6 6 123456789012345678901234567890121234567890123456789012345678901212345 serve the stated objective. (D) suggests a plan of action that, if successful, would help. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 549

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 22. C The original sentence (A) is faulty in two respects. First, it improperly uses because 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 instead of because of. Second, the construction leaves it unclear as to whether the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 modifying phrase already in w ide use refers to other pesticides or to chem ical 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 com positions. (C) corrects the misuse of because by replacing it with due to (an 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 alternative to because of). 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 23. D Instead of using the proper idiom equal . . . to or the proper correlative pair as . . . as, 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the original version attempts to make a comparison by using the improper equal . . . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 as. (D) corrects this error with the correlative pair as . . . as. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 24. E The original sentence (A) uses of twice; the result is wordy and awkward. (E) is 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 idiomatically proper and more concise than the original version. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 25. D Choice (D) weakens the argument by providing some evidence that in this nation it 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 would be comparatively expensive to produce cosmetics with Yucaipa tree-bark oil 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and, accordingly, that the tree population in this nation might not be significantly 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 depleted even if the law were repealed. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 26. A You can rephrase (A) as follows: A ll Web sites administered by individuals holding 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 advanced degrees in educational technology are official Web sites of nationally 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 accredited colleges. In other words, the following two symbolic statements are 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 logically equivalent: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 O nly A are B. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 All B are A. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Given that all Web sites of nationally accredited colleges have received the highest 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 possible rating from the Department, and given that all Web sites administered by 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 individuals holding advanced degrees in educational technology are official Web sites 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 of nationally accredited colleges, it follows logically that all Web sites administered 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 by individuals holding advanced degrees in educational technology have received the 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 highest possible rating from the Department. To follow the logical steps, it helps to 6 123456789012345678901234567890121234567890123456789012345678901212345 express the premises and conclusion symbolically: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: All A are C. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: All B are A. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: All B are C. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 27. E The original version is grammatically correct, but the pronoun reference is vague. (To 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 what does it refer?) (E) clarifies the pronoun reference by using the possessive its 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 lum inosity. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 28. B Exposure to sunlight was mentioned as one factor determining peak bone mass. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Although the passage states that “ many of the factors that affect the attainment of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 peak bone mass also affect rates of bone loss,” it is unwarranted to infer that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 exposure to sunlight is one such factor. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 550 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

AN SWERS 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 29. E As long as the population upon which the cited statistic was based excluded those who 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 had not yet achieved peak bone mass, it does not make a difference whether the men in 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the group achieved their peak bone mass at a different age than the women. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 30. A In lines 12–25, the author lists various factors affecting peak bone mass, then asserts 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 that many of these factors also affect the rate of bone loss. In mentioning pregnancy 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 and lactation as “ additional factors” affecting bone loss, the author implies that these 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 two factors do not also affect peak bone mass. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 31. E The argument relies on two important assumptions. O ne is that the teachers who 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 transferred from Franklin to Valley View were Vining graduates; the other is that 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 teachers who transferred from Valley View to Franklin were not Vining graduates. If 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 12 neither or only one were the case, then it would be unreasonable to conclude that 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Vining graduates are responsible for high academic performance. Admittedly, these 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 assumptions involve a matter of degree; for example, the greater the percentage of 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Vining alumni among the teachers transferring from Franklin to Valley View, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 stronger the argument’s conclusion. And, admittedly, (E) does not acknowledge this 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 fact. N evertheless, (E) provides the essence of one of these two crucial assumptions. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 32. C The argument concludes that the reason for the military’s decision was to reduce pilot 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 error during commercial flights. (C) is the only answer choice that supports this 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 conclusion. Given that chemical warfare is likely to escalate in the future, it would 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 seem that the military would continue to require immunization shots. But the military 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 stopped requiring the shots. So the military’s decision must have been based on some 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 factor outweighing the potential danger of chemical warfare to pilots. O ne such 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 possible factor is the increased danger of commercial airline accidents resulting from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the immunization shots. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 33. A The original sentence contains no grammatical errors, ambiguous references, or 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 idiomatically improper words or phrases. The word visionary, used as an adjective 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 here, is proper, although you could use the word visionaries (a noun) instead. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 34. C The original sentence (A) is unclear in meaning; the use of the word sim ultaneously 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 suggests that two or more items are attained. If the sentence had continued with the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 phrase global and regional dom inance, the use of the word sim ultaneously would 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 have made more sense. (C) excludes the confusing word sim ultaneously and properly 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 sets off the prepositional phrase beginning with in the course with commas to clarify 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the sentence’s meaning. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 551

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 35. E Karl’s response relies on two alternative but interrelated assumptions: (1) the reruns 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are likely to be popular enough to compete with Connie’s favorite program, and (2) 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Connie’s favorite program will not in fact be popular. (E) provides evidence that helps 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 affirm both of these assumptions by suggesting that the reruns might very well be 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 popular enough to draw the viewing audience away from Connie’s favorite program, 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 thus rendering it less popular. Admittedly, (E) would provide even greater support if it 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 explicitly indicated that one popular program can draw viewers away from another. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N evertheless, (E) is the best among the five answer choices. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 36. A The author foresees prolonged inefficiency and misallocation as a consequence of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 gradual, not rapid, privatization (lines 8–11). 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 37. E In the third paragraph the author suggests a willingness to place a private enterprise 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 at risk for the broader purpose of achieving a free-market system. While advocating 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 voucher privatization, the author admits that this approach may very well result in 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the instability of stock prices; yet, the author seems to view the insecurity caused by 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 market pressures as “ good” for private enterprises in that it will drive them to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 efficiency—a sort of sink-or-swim approach. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 38. B The author responds to the skeptics’ claim by pointing out that people are likely to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 weigh the future flow of income from a voucher against the benefits of selling their 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 vouchers now and using the proceeds for consumption. If people were not likely, at least 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 in many cases, to hold their vouchers after weighing these two alternatives, the author 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 would not have made this argument. Thus, the author is implying that, in many cases, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the future flow of income from a voucher will exceed the present value of the voucher. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 39. C Although the author does respond to what might be one undesired result of voucher 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 privatization—falling stock prices, as well as explain the cause of falling stock 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prices—the author does not offer an “ alternative” explanation for this phenomenon, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 as suggested by (C). M oreover, the author’s purpose in discussing falling stock prices 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 is not to explain their cause, but rather to acknowledge that what appears to be an 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 undesirable consequence of voucher privatization may actually help bring about a 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 desirable result. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 40. A The passage indicates that developers have curtailed construction of new office 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 buildings until demand grows to meet supply, while stepping up construction of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 single-family houses. This evidence in itself strongly supports (A). Admittedly, it is 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 possible that an influx of businesses from other states will deplete the current 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 oversupply of office buildings and create sufficient demand for new ones. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 N evertheless, (A) is the best of the five choices. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 41. B The original sentence (A) lacks proper parallelism; to should be omitted. Also, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 original sentence is comprised of two main clauses (each of which could stand on its 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 own as a complete sentences) separated only by a comma. This comma splice should 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 be corrected by inserting an appropriate connecting word, such as but, yet, or 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 although. (B) corrects both problems with the original version. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 552 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

Practice Test

3 1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Analysis of an Issue 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 Question—30 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose a response to the following statement and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 “ M ost great achievements are the result of careful planning and a long, sustained effort 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rather than to sudden bursts of creativity or insight.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 In your view, how accurate is the foregoing statement? Use reasons and/or examples from your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 experience, observation, and/or reading to explain your viewpoint. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 Question—30 Minutes 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions: Using a word processor, compose an essay for the following argument and 6 123456789012345678901234567890121234567890123456789012345678901212345 directive. Do not use any spell-checking or grammar-checking functions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The following appeared in a speech by a prominent state politician: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 “ At Giant Industries, our state’s largest private business, the average production worker is 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 now forty-two years old. Recently, Giant’s revenue from the sale of textiles and paper, 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 which together account for the majority of Giant’s manufacturing business, has declined 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 significantly. Since an increasing percentage of new graduates from our state’s colleges and 6 6 123456789012345678901234567890121234567890123456789012345678901212345 universities are finding jobs in other states, our state will soon face a crisis in which the size 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of our workforce will be insufficient to replace our current workers as they retire, in turn 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 resulting in widespread business failure and a reduced quality of life in our state.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 553

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Discuss how well reasoned you find this argument. In your discussion be sure to analyze the line 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of reasoning and the use of evidence in the argument. For example, you may need to consider 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 what questionable assumptions underlie the thinking and what alternative explanations or 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 counterexamples might weaken the conclusion. You can also discuss what sort of evidence 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 would strengthen or refute the argument, what changes in the argument would make it more 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 logically sound, and what, if anything, would help you better evaluate its conclusion. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 Quantitative Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 37 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Problem Solving Questions: (T hese directions w ill appear on your 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 screen before your first Problem Solving question.) 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Solve this problem and indicate the best of the answer choices given. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 N umbers: All numbers used are real numbers. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Problem Solving question is intended to provide infor6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 mation useful in solving the problem. Figures are drawn as accurately as possible EXCEPT 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 when it is stated in a specific problem that its figure is not drawn to scale. Straight lines 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 may sometimes appear jagged. All figures lie on a plane unless otherwise indicated. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Data Sufficiency Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first D ata Sufficiency question.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 This Data Sufficiency problem consists of a question and two statements, labeled (1) and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2), in which certain data are given. You have to decide whether the data given in the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 statements are sufficient for answering the question. Using the data given in the statements 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 plus your knowledge of mathematics and everyday facts (such as the number of days in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 July or the meaning of counterclock w ise), you must indicate whether: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statement (1) ALO N E is sufficient, but statement (2) alone is not sufficient to answer 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Statement (2) ALO N E is sufficient, but statement (1) alone is not sufficient to answer 6 123456789012345678901234567890121234567890123456789012345678901212345 6 the question asked; 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 BO TH statements (1) and (2) TO GETH ER are sufficient to answer the question asked; 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 but N EITH ER statement ALO N E is sufficient; 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 EACH statement ALO N E is sufficient to answer the question asked; 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Statements (1) and (2) TO GETH ER are N O T sufficient to answer the question asked, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and additional data specific to the problem are needed. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 554 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3

N ote

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N umbers: All numbers used are real numbers. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Figures: A figure accompanying a Data Sufficiency problem will conform to the informa6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tion given in the question, but will not necessarily conform to the additional information 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in statements (1) and (2). 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Lines shown as straight can be assumed to be straight and lines that appear jagged can also 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be assumed to be straight. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 You may assume that positions of points, angles, regions, etc., exist in the order shown and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that angle measures are greater than zero. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 All figures lie in a plane unless otherwise indicated. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 N ote: In Data Sufficiency problems that ask you for the value of a quantity, the data given 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 in the statements are sufficient only when it is possible to determine exactly one numerical 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 value for the quantity. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 To review these directions for subsequent questions of this type, click on H ELP. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Although the questions in this section cover all difficulty levels, you’ll find fewer easy 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 questions than challenging ones. Keep in mind that the GM AT CAT will determine the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 difficulty level of each question based on your responses to prior questions. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a b c d 6 123456789012345678901234567890121234567890123456789012345678901212345 1. If • • • • x 5 1, then x 5 2. Three of four women—A , B, C, and 6 123456789012345678901234567890121234567890123456789012345678901212345 b c d e D —are to be selected randomly to serve 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 on a certain committee. Two of three 6 123456789012345678901234567890121234567890123456789012345678901212345 a 6 A. 123456789012345678901234567890121234567890123456789012345678901212345 men—X , Y , and Z —are to be selected 6 123456789012345678901234567890121234567890123456789012345678901212345 e 6 123456789012345678901234567890121234567890123456789012345678901212345 randomly to serve on the same committee. 123456789012345678901234567890121234567890123456789012345678901212345 66 e 123456789012345678901234567890121234567890123456789012345678901212345 What is the probability that the committee 6 B. 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 will consist of B, C, D , Y , and Z ? a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 C. e 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 12 1 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 a B. 6 123456789012345678901234567890121234567890123456789012345678901212345 9 6 123456789012345678901234567890121234567890123456789012345678901212345 be 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 1 a 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 16 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 9 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 555

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3. Who takes less time to drive to work, 7. What is the value of x ? 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M aria or Lupe? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) x . 0 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) M aria drives to work in 20 minutes. 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) x 2 2 6x 1 9 5 0 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) Lupe and M aria drive the same 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 distance to work. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 8. If b u c 5 u 2 u , what is the value of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 4. The arithmetic mean (average) of two 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 numbers is P 3 Q . If the first number is b c 1 b 2 c? 6 123456789012345678901234567890121234567890123456789012345678901212345 3 3 Q , what is the other number? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 A. 2PQ 2 Q 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 2 6 123456789012345678901234567890121234567890123456789012345678901212345 B. PQ 2 2Q 3 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 2PQ 2 P B. 0 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. P 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. PQ 2 Q 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3 5. What is the minimum value of |a 1 b|? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) |a| 5 3 4 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) |a 2 b| 5 1 6 123456789012345678901234567890121234567890123456789012345678901212345 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 8 6 123456789012345678901234567890121234567890123456789012345678901212345 6. E. 6 123456789012345678901234567890121234567890123456789012345678901212345 R G 6 123456789012345678901234567890121234567890123456789012345678901212345 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 9. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 W 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 In the simple light show pictured above, a 6 123456789012345678901234567890121234567890123456789012345678901212345 In the figure above, if A B i CD , then x 5 6 light starts at the center (white) at time 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 zero and moves once every second in the 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 40 6 123456789012345678901234567890121234567890123456789012345678901212345 following pattern: from white (W ) to blue 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 50 6 123456789012345678901234567890121234567890123456789012345678901212345 (B), back to white, then to green (G ), back 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 60 6 123456789012345678901234567890121234567890123456789012345678901212345 to white, then to red (R ), and back to 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 70 6 123456789012345678901234567890121234567890123456789012345678901212345 white—in a counterclock w ise direction. If 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 80 6 123456789012345678901234567890121234567890123456789012345678901212345 the light continues to move in this way, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 what will be the color sequence from the 6 123456789012345678901234567890121234567890123456789012345678901212345 208th second to the 209th second? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. White to green 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. White to blue 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. White to red 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Red to white 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Green to white 6 1 6 556 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 13. A certain animal shelter houses two different 6 10. Kirk sent $54 to the newspaper dealer for 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 types of animals—dogs and cats. If d repre- 6 whom he delivers papers after deducting a 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 sents the number of dogs, and c the number 6 10% commission for himself. If newspa123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 of cats, which of the following expresses the 6 pers sell for 40 cents each, how many 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 portion of animals at the shelter that are dogs? 6 papers did Kirk deliver? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 d A. 135 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 150 c1d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 160 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 c 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. D. 540 3456789012345678901234567890121234567890123456789012345678901212345 6 12 c 1 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 600 6 123456789012345678901234567890121234567890123456789012345678901212345 c 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 C. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 11. If x 1 y 5 a, and if x 2 y 5 b, then x 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 c 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. A. 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (a 1 b) d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 c 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. d 1 B. a 1 b 6 123456789012345678901234567890121234567890123456789012345678901212345 d 6 123456789012345678901234567890121234567890123456789012345678901212345 C. a 2 b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 14. 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 D. ab 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 E. (a 2 b) 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 12. Four of the five interior angles of a 6 123456789012345678901234567890121234567890123456789012345678901212345 pentagon measure 110°, 60°, 120°, and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 100°. What is the measure of the fifth 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 interior angle? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 100° 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Based on the table above, if the total har- 6 B. 110° 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 vested crop revenues for Willot and Tilson C. 125° 6 123456789012345678901234567890121234567890123456789012345678901212345 counties combined equaled those for Stanton 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 135° 6 123456789012345678901234567890121234567890123456789012345678901212345 and O sher counties combined, then Stanton 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 150° 6 123456789012345678901234567890121234567890123456789012345678901212345 County’s subsidized farm revenues accounted 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for what percentage of the total harvested 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 crop revenues for all four counties? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) During year X, O sher County’s total 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 harvested crop revenues totaled twice 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 those of Tilson County. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) During year X, Tilson County’s farms 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 contributed 18% of all harvested crop 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 revenues for the four counties. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 557

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 15. 17. M college students agree to rent an 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 apartment for D dollars per month, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 sharing the rent equally. If the rent is 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 increased by $100, what amount must 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 each student contribute? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 D 1 100 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 1 100 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D 3456789012345678901234567890121234567890123456789012345678901212345 6 12 In the figure above, the centers of all three C. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M 3456789012345678901234567890121234567890123456789012345678901212345 6 12 circles lie on the same line. The radius of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the middle-sized circle is twice that of the M 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6 123456789012345678901234567890121234567890123456789012345678901212345 smallest circle. If the radius of the smallest D 1 100 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 circle is 1, what is the length of the 6 123456789012345678901234567890121234567890123456789012345678901212345 M 1 100 6 123456789012345678901234567890121234567890123456789012345678901212345 boundary of the shaded region? E. 6 123456789012345678901234567890121234567890123456789012345678901212345 D 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 9 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. 3p 18. If n is a positive even integer, and if n 4 3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 12 results in a quotient with a remainder of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 6p 1, which of the following expressions is 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. 12p N O T divisible by 3? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. n 1 2 6 123456789012345678901234567890121234567890123456789012345678901212345 16. If am 5 b n , and if a Þ b Þ m Þ n, what is 6 123456789012345678901234567890121234567890123456789012345678901212345 B. n 1 5 6 123456789012345678901234567890121234567890123456789012345678901212345 the value of a 1 b 1 m 1 n? 6 123456789012345678901234567890121234567890123456789012345678901212345 C. n 2 1 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) a, b, m , and n are all non-negative 6 123456789012345678901234567890121234567890123456789012345678901212345 D. n 3 2 6 123456789012345678901234567890121234567890123456789012345678901212345 integers less than 10. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. n 3 3 6 123456789012345678901234567890121234567890123456789012345678901212345 n 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) b 5 81. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 a a 19. 6 123456789012345678901234567890121234567890123456789012345678901212345 1 5 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 b b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a2 A. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 a 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 a4 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. a a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 b b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. a=2 6 1 6 b 558 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3 23. Each computer system in a graphic-arts 20. Is it true that = 6 123456789012345678901234567890121234567890123456789012345678901212345 a , a? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 classroom is equipped with either a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) a , 0 scanner, a printer, or both. What percent123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 age of the computer systems are equipped 6 (2) a . 2 1 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 with scanners but not printers? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 21. A certain purse contains 30 coins. Each 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 (1) 20 percent of the computer systems 3456789012345678901234567890121234567890123456789012345678901212345 6 12 coin is either a nickel or a quarter. If the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are equipped with both scanners and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 total value of all coins in the purse is 6 123456789012345678901234567890121234567890123456789012345678901212345 printers. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 $4.70, how many nickels does the purse 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) 25 percent of the computer systems contain? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 are equipped with printers but not 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 with scanners. B. 14 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 16 3456789012345678901234567890121234567890123456789012345678901212345 6 12 24. Daniel, Carl, and Todd working together 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 20 6 123456789012345678901234567890121234567890123456789012345678901212345 can load a moving van in 8 hours. H ow 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 22 6 123456789012345678901234567890121234567890123456789012345678901212345 long would it take Daniel working alone 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to load the van? 6 123456789012345678901234567890121234567890123456789012345678901212345 22. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) Working alone, Carl can load the van 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 in 15 hours. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) Carl and Todd working together can 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 load the van in 12 hours. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 25. What is the unit area of circle O on the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 standard x y-coordinate plane? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 O nce a month, a crop duster sprays a 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) Point R (7,23) and point S(7,7) both 6 123456789012345678901234567890121234567890123456789012345678901212345 triangular area defined by three farm 123456789012345678901234567890121234567890123456789012345678901212345 lie along the circumference of circle O . 6 6 123456789012345678901234567890121234567890123456789012345678901212345 houses—A , B, and C—as indicated in the 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) R and S are the endpoints of the 6 123456789012345678901234567890121234567890123456789012345678901212345 figure above. Farmhouse B lies due west of 6 123456789012345678901234567890121234567890123456789012345678901212345 longest possible chord of circle O . 6 123456789012345678901234567890121234567890123456789012345678901212345 Farmhouse C. Given the compass direc6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 tions and distances (in miles) indicated in 6 123456789012345678901234567890121234567890123456789012345678901212345 26. If A and B denote the digits of a threethe figure, what is the total area that the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 digit number BAB, is BAB divisible by 4? 6 crop duster sprays? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (1) The product of A and B is divisible (1) Farmhouse C is located 4 miles further 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 by 4. south than farmhouse A . 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) The sum of B, A, and B is divisible 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) Farmhouse C is located 10 miles 6 123456789012345678901234567890121234567890123456789012345678901212345 by 4. 6 123456789012345678901234567890121234567890123456789012345678901212345 further east than farmhouse A . 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 559

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 29. Which of the following is the approximate 6 27. If a total of 55 books were sold at a 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ratio of the average number of hours per community book fair, and if each book 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 week that the youngest age group spent was either hardback or paperback, how 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 watching entertainment on television to many hardback books were sold at the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the average number of hours that the book fair? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 other two groups combined spent watch- 6 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) The total proceeds from the sale of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ing the same type of programming? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 paperback books, each of which was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 3:4 sold for 75 cents, was $19.50. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 1:1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (2) The proceeds from the book fair 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 4:3 6 123456789012345678901234567890121234567890123456789012345678901212345 totaled $48.50. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. 5:3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 3:2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Questions 28 and 29 refer to the following 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 figure: 30. If a portion of $10,000 is invested at 6% 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and the remaining portion is invested at 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5% , and if x represents the amount 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 invested at 6% , what is the annual income 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 in dollars from the 5% investment? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. .05(10,000 2 x ) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. .05(x 1 10,000) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. 5(x 2 10,000) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 5(10,000 2 x ) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. .05(x 2 10,000) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 31. In a geometric series, each term is a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 constant multiple of the preceding one. If 28. According to the graph, the two age 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the first three terms in a geometric series groups, other than the group that spent 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 are 22, x , and 28, which of the following the greatest number of hours per week 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 could be the sixth term in the series? watching sports on television, accounted 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for approximately what percent of the 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 2128 6 123456789012345678901234567890121234567890123456789012345678901212345 total hours spent watching television 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 217 6 123456789012345678901234567890121234567890123456789012345678901212345 among all three age groups? 6 123456789012345678901234567890121234567890123456789012345678901212345 C. 64 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. 256 A. 27 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 512 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 36 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. 60 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 76 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 85 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 560 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 32. What is the maximum number of rectan35. Two buses are 515 miles apart. At 9:30 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 gular boxes, each measuring 2 inches by 3 a.m., they start traveling toward each 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 inches by 5 inches, that can be packed into other at rates of 48 and 55 miles per hour. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 a rectangular packing box measuring 18 At what time will they pass each other? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 inches by 19 inches by 35 inches, if all of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 1:30 p.m. 6 123456789012345678901234567890121234567890123456789012345678901212345 the smaller boxes are aligned in the same 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. 2:00 p.m. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 direction? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 2:30 p.m. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 A. 296 D. 3:00 p.m. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. 356 E. 3:30 p.m. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 378 6 123456789012345678901234567890121234567890123456789012345678901212345 77 76 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 7 27 D. 412 3456789012345678901234567890121234567890123456789012345678901212345 6 12 36. 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 424 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. 7 3456789012345678901234567890121234567890123456789012345678901212345 6 12 33. If J is a set of six integers, what is the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 77 B. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 7 76 median value of those integers? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. 49 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (1) The difference between the least and 75 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. 7 3456789012345678901234567890121234567890123456789012345678901212345 6 12 greatest integers in set J is 40. 76 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. 7 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (2) The arithmetic mean (average) of the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 37. An investor can sell her M icroTron stock 6 six integers in set J is 15. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 for $36 per share and her Dynaco stock 6 123456789012345678901234567890121234567890123456789012345678901212345 34. 6 for $52 per share. If she sells 300 shares 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 altogether, some of each stock, at an 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 average price per share of $40, how many 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 shares of Dynaco stock has she sold? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. 52 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. 75 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. 92 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. 136 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. 184 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 In the figure above, is the area of the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 shaded region less than the combined area 6 123456789012345678901234567890121234567890123456789012345678901212345 of the two triangles? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (1) x 5 60. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (2) The length of chord A B equals the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 circle’s radius. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 561

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 41 Questions—75 Minutes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Directions for Sentence Correction Questions: (T hese directions w ill appear on your 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Sentence Correction question.) 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 This question presents a sentence, all or part of which is underlined. Beneath the sentence 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 you will find five ways of phrasing the underlined part. The first of these repeats the 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 original; the other four are different. If you think the original is best, choose the first 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 answer; otherwise choose one of the others. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 This question tests correctness and effectiveness of expression. In choosing your answer, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 follow the requirements of Standard Written English; that is, pay attention to grammar, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 choice of words, and sentence construction. Choose the answer that produces the most 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 effective sentence; this answer should be clear and exact, without awkwardness, ambigu6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ity, redundancy, or grammatical error. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Critical Reasoning Questions: (T hese directions w ill appear on your 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 screen before your first Critical R easoning question.) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 For this question, select the best of the answer choices given. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Directions for Reading Comprehension Questions: (T hese directions w ill appear on 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 your screen before your first group of R eading Com prehension questions.) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The questions in this group are based on the content of a passage. After reading the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 passage, choose the best answer to each question. Answer all the questions following the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 passage on the basis of what is stated or im plied in the passage. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2. T he R eluctant M onarch, which Francis 1. N ot only smoking cigarettes but also cigar 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 smoking has been banned now from many Craig wrote as her third in a series of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 public places. books about the British M onarchy. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. N ot only smoking cigarettes but also A. T he R eluctant M onarch, which 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 cigar smoking has been banned now Francis Craig wrote as her third 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. Cigarette smoking and cigar smoking B. T he R eluctant M onarch is the third 6 123456789012345678901234567890121234567890123456789012345678901212345 are both banned now book written by Francis Craig 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. N ot only has smoking cigarettes been C. Written by Francis Craig, T he R eluc- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 banned but so has cigar smoking tant M onarch, which is her third book 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Both smoking cigarettes and cigar D. Francis Craig wrote T he R eluctant 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 smoking is now banned M onarch, which book is her third 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. Smoking cigarettes as well as cigars is E. T he R eluctant M onarch, written by 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 now banned Francis Craig, is her third 6 1 6 562 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 5. John: If a person believes in the inevitabil- 6 3. Some varieties of parrots live as long as 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ity of success, then that person will surely 6 the age of one hundred years. 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 succeed. 6 123456789012345678901234567890121234567890123456789012345678901212345 A. as long as the age of one hundred years 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Jolanda: I disagree. According to a recent B. as long as one hundred 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 magazine article entitled “ The 100 M ost C. as long as one hundred years old 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Successful Women in H istory,” most of D. as long as one hundred years 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 these 100 women did not believe they E. to be one hundred years old in age 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 would ever become successful. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 4. Two years ago, a court found a certain ciga3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following would be John’s 3456789012345678901234567890121234567890123456789012345678901212345 6 rette manufacturer legally liable for the 12 6 123456789012345678901234567890121234567890123456789012345678901212345 most logically convincing response to deaths of several thousand people who 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Jolanda’s counter-argument above? smoked the company’s cigarettes, and or3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Success does not depend on whether a dered the company to pay a large sum to the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 person believes in its inevitability. families of those victims. The next year, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Successful people are often viewed by company’s profits increased to record lev123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 others as unsuccessful. els. The lesson for other large corporations 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Success is inevitable for some people is clear: Produce products that are unsafe or 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 but not for others. unhealthy for consumers, and your com6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Society’s definition of success might pany will become more profitable. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 have changed throughout history. 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if true, would 6 123456789012345678901234567890121234567890123456789012345678901212345 E. N one of the successful people listed in 6 123456789012345678901234567890121234567890123456789012345678901212345 provide the best reason for rejecting the 6 123456789012345678901234567890121234567890123456789012345678901212345 the magazine article were men. 6 123456789012345678901234567890121234567890123456789012345678901212345 conclusion drawn in the last sentence 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 above? 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 6–8 are based on the following 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Publicity resulting from court 6 123456789012345678901234567890121234567890123456789012345678901212345 passage: 6 123456789012345678901234567890121234567890123456789012345678901212345 judgments against large businesses 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Line The decline of the Iroquois Indian often affects their profitability. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 nations began during the American B. M anufacturers of potentially unsafe 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Revolution of 1776, when disagreement 6 or unhealthy products are required by 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 among them as to whether they should law to provide appropriate warnings 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 become involved in the war began to (5) to consumers. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 divide the Iroquois. Because of the C. M anufacturers of dangerous products 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 success of the revolutionaries and the are often held liable for injuries to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 encroachment upon Iroquois lands that consumers resulting from the use of 6 123456789012345678901234567890121234567890123456789012345678901212345 followed, many Iroquois resettled in 6 123456789012345678901234567890121234567890123456789012345678901212345 those products. 6 123456789012345678901234567890121234567890123456789012345678901212345 Canada, while those who remained (10) 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The risks involved in using any 6 123456789012345678901234567890121234567890123456789012345678901212345 behind lost the respect they had enjoyed 6 123456789012345678901234567890121234567890123456789012345678901212345 product are just one of many types of 6 123456789012345678901234567890121234567890123456789012345678901212345 among other Indian nations. The 6 123456789012345678901234567890121234567890123456789012345678901212345 factors consumers consider when 6 123456789012345678901234567890121234567890123456789012345678901212345 introduction of distilled spirits resulted in buying a product. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 widespread alcoholism, leading in turn to 6 E. Compared to cigarettes, most 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the rapid decline of both the culture and (15) consumer products pose insignificant 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 population. The influence of the Q uakers risks to the health or safety of those 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 impeded, yet in another sense contribwho use them. 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 563

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 7. Among the following reasons, it is most uted, to this decline. By establishing 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 likely that the author considers H andsome 6 schools for the Iroquois and by introduc3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Lake’s leading a rival of the Iroquois ing them to modern technology for (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 culture to be “ ironic” because agriculture and husbandry, the Q uakers 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 instilled in the Iroquois some hope for 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. he was a former member of the Great 6 123456789012345678901234567890121234567890123456789012345678901212345 the future yet undermined the Iroquois’ 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Council. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 sense of national identity. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. he was not a full-blooded relative of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Ironically, it was H andsome Lake (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 Seneca Cornplanter. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 who can be credited with reviving the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. he was related by blood to an 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Iroquois culture. Lake, the alcoholic 3456789012345678901234567890121234567890123456789012345678901212345 6 12 important proponent of assimilation. 6 123456789012345678901234567890121234567890123456789012345678901212345 half-brother of Seneca Cornplanter, 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. Seneca Cornplanter was Lake’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 perhaps the most outspoken proponent 3456789012345678901234567890121234567890123456789012345678901212345 6 12 alcoholic half-brother. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 among the Iroquois for assimilation of (30) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. his religious beliefs conflicted with 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 white customs and institutions, was a 6 123456789012345678901234567890121234567890123456789012345678901212345 traditional Iroquois beliefs. 6 123456789012345678901234567890121234567890123456789012345678901212345 former member of the Great Council of 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Iroquois nations. Inspired by a near8. Assuming that the reasons asserted by the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 death vision in 1799, Lake established a author for the decline of the Iroquois 6 123456789012345678901234567890121234567890123456789012345678901212345 new religion among the Iroquois which (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 culture are historically representative of 6 123456789012345678901234567890121234567890123456789012345678901212345 tied the more useful aspects of Christian123456789012345678901234567890121234567890123456789012345678901212345 the decline of cultural minorities, which of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 ity to traditional Indian beliefs and 6 123456789012345678901234567890121234567890123456789012345678901212345 the following developments would most 6 123456789012345678901234567890121234567890123456789012345678901212345 customs. 6 123456789012345678901234567890121234567890123456789012345678901212345 likely contribute to the demise of a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 modern-day ethnic minority? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6. The passage mentions all the following 6 123456789012345678901234567890121234567890123456789012345678901212345 A. A bilingual education program in 6 123456789012345678901234567890121234567890123456789012345678901212345 events as contributing to the decline of the 6 which children who are members of 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Iroquois culture EXCEPT: the minority group learn to read and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 write in both their traditional A. new educational opportunities for the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 language and the language prevalent Iroquois people. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in the present culture. B. divisive power struggles among the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. A tax credit for residential-property leaders of the Iroquois nations. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 owners who lease their property to C. introduction of new farming technolo123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 members of the minority group. gies. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Increased efforts by local government D. territorial threats against the Iroquois 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to eradicate the availability of illegal nations. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 drugs. E. discord among the nations regarding 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The declaration of a national holiday their role in the American Revolution. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 commemorating a past war in which the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 minority group played an active role. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 E. A government-sponsored program to 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 assist minority-owned businesses in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 using computer technology to 6 123456789012345678901234567890121234567890123456789012345678901212345 improve efficiency. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 564 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 11. When people are worried about general 9. O ver thirty million illegal immigrants live 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 economic conditions, they tend to spend in the United States, including greater than 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 less on consumer goods. O fficial governtwo million alone in California. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 ment figures show that retail inventory 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. greater than two million alone in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 levels throughout the economy have been 3456789012345678901234567890121234567890123456789012345678901212345 6 12 California. 6 123456789012345678901234567890121234567890123456789012345678901212345 increasing in recent months. H owever, 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. in California greater than two million. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 consumer-confidence levels are currently 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. more in California than two million. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the highest they’ve been in several years. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. more than two million in California 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Any of the following, if true, would help alone. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to explain the apparent discrepancy E. greater than two million such illegal 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 described above EXCEPT: immigrants in California. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. H igh interest rates tend to discourage 6 3456789012345678901234567890121234567890123456789012345678901212345 12 10. Babies who are breast fed instead of bottle 3456789012345678901234567890121234567890123456789012345678901212345 6 12 consumers from buying products on 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fed until at least their first birthday are 6 123456789012345678901234567890121234567890123456789012345678901212345 credit that they otherwise could not 6 123456789012345678901234567890121234567890123456789012345678901212345 seventy percent less likely to become obese 6 123456789012345678901234567890121234567890123456789012345678901212345 afford. 6 123456789012345678901234567890121234567890123456789012345678901212345 children than babies who are bottle fed 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Businesses often increase production 6 123456789012345678901234567890121234567890123456789012345678901212345 but not breast fed. A child is obese if the 6 123456789012345678901234567890121234567890123456789012345678901212345 of consumer goods in anticipation of 6 123456789012345678901234567890121234567890123456789012345678901212345 ratio of the child’s weight to height is 6 123456789012345678901234567890121234567890123456789012345678901212345 improving economic conditions. 6 123456789012345678901234567890121234567890123456789012345678901212345 among the highest three percent of all 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Consumer-spending levels tend to 6 123456789012345678901234567890121234567890123456789012345678901212345 children. But breast feeding instead of 6 123456789012345678901234567890121234567890123456789012345678901212345 follow seasonal patterns. 6 123456789012345678901234567890121234567890123456789012345678901212345 bottle feeding during the first three 123456789012345678901234567890121234567890123456789012345678901212345 D. When the domestic currency’s value 6 6 123456789012345678901234567890121234567890123456789012345678901212345 months of a baby’s life also reduces the 6 123456789012345678901234567890121234567890123456789012345678901212345 increases compared to that of foreign 6 123456789012345678901234567890121234567890123456789012345678901212345 likelihood that the baby will become an 6 123456789012345678901234567890121234567890123456789012345678901212345 currencies, foreign products become 6 123456789012345678901234567890121234567890123456789012345678901212345 obese child. 6 123456789012345678901234567890121234567890123456789012345678901212345 less expensive for domestic consumers. 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following can be most 123456789012345678901234567890121234567890123456789012345678901212345 E. Increased business spending generally 6 6 123456789012345678901234567890121234567890123456789012345678901212345 properly inferred from the information in 6 123456789012345678901234567890121234567890123456789012345678901212345 precedes a decline in consumer 6 123456789012345678901234567890121234567890123456789012345678901212345 the passage? 6 123456789012345678901234567890121234567890123456789012345678901212345 confidence levels. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. Genetic propensity for obesity is not 6 123456789012345678901234567890121234567890123456789012345678901212345 12. Ignorance of the law does not preclude 6 123456789012345678901234567890121234567890123456789012345678901212345 significant in determining whether a 6 123456789012345678901234567890121234567890123456789012345678901212345 one being arrested for violating it. 6 123456789012345678901234567890121234567890123456789012345678901212345 baby will become an obese child. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. Bottle feeding is more likely than breast A. one being arrested for violating it 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 feeding to result in obesity in children. B. arrest for one’s violation of it 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. Unless a baby is breast fed instead of C. one’s violation and arrest for it 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 bottle fed until at least its first D. one from being arrested for violating 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 birthday, the baby is likely to become that law 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 an obese child. E. one from an arrest for having violated 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. If a child is obese, there is a seventythe law 6 123456789012345678901234567890121234567890123456789012345678901212345 percent likelihood that, as a baby, the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 child was bottle fed but not breast fed. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Breast feeding is ineffective to prevent 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 obesity unless it is continued until at 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 least the baby’s first birthday. 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 565

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 since the fresh surface was made. But this 6 13. Rationalizing the protracted and bloody 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 method failed to account for the chemical 6 (15) war with the Philippines, President 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 variability in the physical and chemical M cKinley described the process of 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 mechanism of obsidian hydration. subjugating the Filipinos as “ benign 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 M oreover, each geographic source assimilation.” 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 presented unique chemical characteris6 123456789012345678901234567890121234567890123456789012345678901212345 A. Rationalizing the protracted and 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tics, necessitating a trace element analysis (20) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 bloody war 3456789012345678901234567890121234567890123456789012345678901212345 6 12 for each such source. 6 123456789012345678901234567890121234567890123456789012345678901212345 B. To rationalize the protracted war and 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Yet despite its limitations, obsidian 3456789012345678901234567890121234567890123456789012345678901212345 6 12 bloody war 3456789012345678901234567890121234567890123456789012345678901212345 6 12 dating helped archeologists identify the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. The protracted and bloody war was 6 123456789012345678901234567890121234567890123456789012345678901212345 sources of many obsidian artifacts, and 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 rationalized 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to identify in turn ancient exchange (25) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. Rationalizing the war, which was 3456789012345678901234567890121234567890123456789012345678901212345 6 12 networks for the flow of goods. N or 3456789012345678901234567890121234567890123456789012345678901212345 6 12 protracted as well as bloody 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 were ceramic studies and fluoride 6 123456789012345678901234567890121234567890123456789012345678901212345 E. To rationalize the war, a protracted 6 123456789012345678901234567890121234567890123456789012345678901212345 analysis supplanted entirely by the and bloody one 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 radiocarbon method, which in use allows 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 for field labeling and laboratory errors, (30) 14. Cambodia remains being a largely 6 123456789012345678901234567890121234567890123456789012345678901212345 as well as sample contamination. In 6 123456789012345678901234567890121234567890123456789012345678901212345 underdeveloped country because virtually 6 123456789012345678901234567890121234567890123456789012345678901212345 addition, in the 1970s dendrochronologi6 123456789012345678901234567890121234567890123456789012345678901212345 all educated citizens were slaughtered 6 123456789012345678901234567890121234567890123456789012345678901212345 cal (tree-ring) studies on the bristlecone 6 123456789012345678901234567890121234567890123456789012345678901212345 during the regime of Pon Pen. 6 123456789012345678901234567890121234567890123456789012345678901212345 pine showed that deviation from radio123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 A. remains being carbon values increases as one moves (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. is still remaining back in time. Eventually calibration 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. is being curves were developed to account for this 6 123456789012345678901234567890121234567890123456789012345678901212345 6 D. remains 123456789012345678901234567890121234567890123456789012345678901212345 phenomenon; but in the archeological 6 123456789012345678901234567890121234567890123456789012345678901212345 E. remains still 6 123456789012345678901234567890121234567890123456789012345678901212345 literature we still find dual references to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 radiocarbon and sidereal, or calendar, (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 time. Questions 15–17 are based on the following 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 passage: 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 15. Based on the information in the passage, 6 123456789012345678901234567890121234567890123456789012345678901212345 Line For absolute dating of archeological 6 123456789012345678901234567890121234567890123456789012345678901212345 which of the following is LEAST likely to 6 123456789012345678901234567890121234567890123456789012345678901212345 artifacts, the radiocarbon method 123456789012345678901234567890121234567890123456789012345678901212345 have been a means of dating archeological 6 emerged during the latter half of the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 artifacts? twentieth century as the most reliable 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and precise method. The results of (5) 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Ceramics studies 6 123456789012345678901234567890121234567890123456789012345678901212345 obsidian (volcanic glass) dating, a 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Radiocarbon dating 6 123456789012345678901234567890121234567890123456789012345678901212345 method based on the belief that newly 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Dendrochronological studies 6 123456789012345678901234567890121234567890123456789012345678901212345 exposed obsidian surfaces absorb 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Fluoride analysis 6 123456789012345678901234567890121234567890123456789012345678901212345 moisture from the surrounding atmo6 123456789012345678901234567890121234567890123456789012345678901212345 E. O bsidian hydration-layer analysis 6 123456789012345678901234567890121234567890123456789012345678901212345 sphere at a constant rate, proved uneven. (10) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 It was initially thought that the thickness 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of the hydration layer would provide a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 means of calculating the time elapsed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 566 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 18. When inhaled, asbestos fibers are known 16. In the passage, the author mentions all of 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to significantly increase the likelihood of the following as problems with radiocar3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 lung cancer and other respiratory ailbon dating EXCEPT: 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 ments. Thousands of buildings in this 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. disparities with the calendar dating 3456789012345678901234567890121234567890123456789012345678901212345 6 12 state, especially apartment houses, are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 system. 6 123456789012345678901234567890121234567890123456789012345678901212345 insulated with asbestos. Some local 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. deterioration of samples. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 governments in the state have initiated 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. identification errors by archeological 3456789012345678901234567890121234567890123456789012345678901212345 6 12 massive and costly efforts to remove this 6 123456789012345678901234567890121234567890123456789012345678901212345 field workers. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 asbestos. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. contamination of artifacts. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, taken E. mistakes by laboratory workers. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 together with the information above, best 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 17. With which of the following statements 3456789012345678901234567890121234567890123456789012345678901212345 12 supports the conclusion that the health of 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 would the passage’s author most likely 3456789012345678901234567890121234567890123456789012345678901212345 12 those who occupy the buildings would be 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 agree? 123456789012345678901234567890121234567890123456789012345678901212345 better preserved by leaving the asbestos in 6 6 123456789012345678901234567890121234567890123456789012345678901212345 place than by removing it? 6 123456789012345678901234567890121234567890123456789012345678901212345 A. The greater the time that has elapsed 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 since exposure of obsidian surface to A. In removing the asbestos, millions of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 moisture the less reliable the results of fibers are likely to be dislodged and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 obsidian dating. sent into circulation in the air. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. The hydration layer accumulating B. Asbestos removal is a hazardous 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 through obsidian moisture absorption procedure, posing significant health 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 varies in thickness depending on the dangers to those who perform it. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 amount of surface area exposed to C. Fewer than one person in a hundred 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 moisture. who breathes asbestos-contaminated 6 123456789012345678901234567890121234567890123456789012345678901212345 6 C. The unpredictability of the obsidian 123456789012345678901234567890121234567890123456789012345678901212345 air is likely to contract a respiratory 6 123456789012345678901234567890121234567890123456789012345678901212345 hydration process renders the 6 123456789012345678901234567890121234567890123456789012345678901212345 ailment as a result. 6 123456789012345678901234567890121234567890123456789012345678901212345 obsidian dating method problematic 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Apartment dwellers typically move 6 123456789012345678901234567890121234567890123456789012345678901212345 as a means of determining historical 6 123456789012345678901234567890121234567890123456789012345678901212345 from one residence to another more 6 123456789012345678901234567890121234567890123456789012345678901212345 trade routes. 6 123456789012345678901234567890121234567890123456789012345678901212345 frequently than people who live in 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The results of obsidian dating are as single family homes. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reliable and precise as those of E. M ost people who live in apartment 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fluoride analysis only if trace element buildings insulated with asbestos are 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 analysis is performed for the geoaware of that fact. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 graphic source of the obsidian. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. An obsidian artifact can be reliably 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 dated using the obsidian method only 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 if certain environmental conditions 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 where the artifact was found are 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 considered. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 567

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 20. The emission of fluorocarbons into the 19. O ver the last year, the price that toy 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 earth’s atmosphere has been shown to manufacturer FunTime charges for each 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 deplete the ozone layer in the atmosphere. toy it produces and sells directly to 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Therefore, if we were to eliminate all consumers has, on average, nearly 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 sources of fluorocarbon emission, we doubled, prompting complaints to the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 could successfully halt ozone layer company by many consumers. To combat 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 depletion. this problem, FunTime’s management 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 must make every effort to improve 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following demonstrates a 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 relations with its union workers in order 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pattern of reasoning that is most similar to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to help prevent them from striking, as 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the flawed reasoning in the argument 6 123456789012345678901234567890121234567890123456789012345678901212345 these workers did for several weeks during 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 above? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the past year. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. When challenged to prove their 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, would cast psychic abilities, several of the world’s 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the most doubt on the effectiveness of the most celebrated so-called psychics 6 123456789012345678901234567890121234567890123456789012345678901212345 proposal suggested above? 6 123456789012345678901234567890121234567890123456789012345678901212345 were unable to do so, clearly proving 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 that the psychic phenomenon is A. Despite the complaints from consum6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fiction rather than fact. ers, sales of FunTime toys directly to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. The theory that the earth’s temperature 6 consumers have increased steadily 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 would be shown to be cyclical if mea- 6 over the last year. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 sured over millions of years is convincB. FunTime’s union workers are likely to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ing, in light of the fact that the extinc- 6 be skeptical of any attempt by 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 tion of the dinosaurs occurred due to 6 management to improve its relations 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 changes in the earth’s temperature. with them. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. Flag burning is ultimately in the C. Some consumers who buy FunTime 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 state’s interest as well as the individu- 6 toys don’t mind paying more for them 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 al’s interest, because the First Amendbecause they are the highest quality 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ment right to free expression was toys available. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 created for the purpose of preserving D. FunTime’s union workers are likely to 6 123456789012345678901234567890121234567890123456789012345678901212345 our democratic way of life. strike again in the near future, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Any person suffering from phlebitis 6 regardless of management’s efforts to 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 must take the drug Anatol in order to 6 improve relations with them. 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prevent the condition from worsening, 6 E. M ost of the increase in the prices of 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 as evidenced by the fact that doctors 6 FunTime toys is attributable to an 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 have used Anatol successfully for many 6 increase in the cost of the raw 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 years to treat and control phlebitis. materials the company uses to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. Autopsies of the residents of H uiki manufacture its toys. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Island killed by a recent volcanic 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 eruption have shown excessive bone 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 deterioration, which leads to my 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 conclusion that the H uikan culture 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 encourages a diet that promotes bone 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 marrow disease. 6 1 6 568 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 22. Upon man-made toxins’ invading the 21. A dvertising ex ecutive: Those who oppose 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the use of humor in advertising, whether human body, special enzymes are de3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 print and television, either lack a sense of ployed, rebuilding any damaged DN A 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 humor or fail to understand the advantage strands that result. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of using humor to advertise a product or 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. Upon man-made toxins invading the 6 123456789012345678901234567890121234567890123456789012345678901212345 service. After all, numerous surveys show 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 human body, special enzymes are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 that ordinary consumers are almost twice 3456789012345678901234567890121234567890123456789012345678901212345 6 12 deployed, rebuilding any damaged 3456789012345678901234567890121234567890123456789012345678901212345 6 12 as likely to recall a humorous commercial 6 123456789012345678901234567890121234567890123456789012345678901212345 DN A strands that result. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 as they are to recall a serious commercial. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. Upon man-made toxins, invasion of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Which of the following, if true, would cast the human body, special enzymes are 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 the most serious doubt on the accuracy of deployed that rebuild any damaged 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the advertising executive’s contention? DN A strands resulting from the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 invasion. A. Although most consumers surveyed 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. When man-made toxins invade the were able to recall viewing humorous 3456789012345678901234567890121234567890123456789012345678901212345 6 12 human body, special enzymes are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 commercials, many said they enjoyed 3456789012345678901234567890121234567890123456789012345678901212345 6 12 deployed to rebuild any DN A strands 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the serious commercials more. 6 123456789012345678901234567890121234567890123456789012345678901212345 damaged as a result. 6 123456789012345678901234567890121234567890123456789012345678901212345 B. For certain types of products, 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Special enzymes are deployed when6 123456789012345678901234567890121234567890123456789012345678901212345 humorous advertising would be 6 123456789012345678901234567890121234567890123456789012345678901212345 ever man-made toxins invade the 6 123456789012345678901234567890121234567890123456789012345678901212345 inappropriate and potentially offen6 123456789012345678901234567890121234567890123456789012345678901212345 human body; they rebuild any damage 6 123456789012345678901234567890121234567890123456789012345678901212345 sive. 6 123456789012345678901234567890121234567890123456789012345678901212345 that results to DN A strands. 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Although most consumers surveyed 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Damage to DN A strands that results 6 123456789012345678901234567890121234567890123456789012345678901212345 were able to recall viewing humorous 6 123456789012345678901234567890121234567890123456789012345678901212345 when man-made toxins invade the 6 123456789012345678901234567890121234567890123456789012345678901212345 commercials, most failed to recall the 123456789012345678901234567890121234567890123456789012345678901212345 human body are repaired by deployed 6 6 123456789012345678901234567890121234567890123456789012345678901212345 name of the product advertised. 6 123456789012345678901234567890121234567890123456789012345678901212345 special enzymes. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The consumers surveyed about 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 humorous commercials included 23. The fact that the tie between the M anchus 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 people considered unlikely to buy the and the Chinese was cultural rather than 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 particular product advertised. racial helps to account for the homogene6 123456789012345678901234567890121234567890123456789012345678901212345 E. The use of humorous television 6 123456789012345678901234567890121234567890123456789012345678901212345 ity of the Chinese people. 6 123456789012345678901234567890121234567890123456789012345678901212345 commercials by advertisers has been 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. cultural rather than racial helps to declining over the last few years. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 account for 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. not racial but cultural in nature helps 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 explain 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. a cultural tie but not racial helps 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 explain 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 D. cultural rather than a racial one helps 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to explain 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. cultural rather than a racial tie helps 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to account for 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 569

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 25. Although the use of fertilizers tends to 24. The atmospheric study reported last 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 diminish the flavor of fruits, the use of month in the Journal of the Environment 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 pesticides makes virtually no difference in would not have been taken seriously by 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 flavor, assuming the fruit is washed the scientific community if they were 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 thoroughly. M oreover, the use of pesticognizant of the questionable methodol3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 cides repels insects that would otherwise ogy employed. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 leave unsightly blemishes on the fruit. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. have been taken seriously by the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Therefore, in the interest of appealing to 6 123456789012345678901234567890121234567890123456789012345678901212345 scientific community if they were 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 consumer tastes, fruit growers would be 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. be taken seriously by the scientific 3456789012345678901234567890121234567890123456789012345678901212345 6 12 well advised to use pesticides but not 3456789012345678901234567890121234567890123456789012345678901212345 6 12 community in the event that it had 6 123456789012345678901234567890121234567890123456789012345678901212345 artificial fertilizers. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 become 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following, if true, could C. have been taken seriously by the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 proponents of the argument most approscientific community were they 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 priately cite as evidence for the soundness 6 D. have been taken seriously by the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of the advice to fruit growers given in the 6 scientific community when the 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 last sentence? scientific community became 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 E. have been taken seriously by the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. The use of natural fertilizer results in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 scientific community had scientists 3456789012345678901234567890121234567890123456789012345678901212345 6 12 larger, more colorful fruit than the use 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 been 6 123456789012345678901234567890121234567890123456789012345678901212345 of artificial fertilizer. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. The use of pesticides and fertilizers 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 increase fruit growers’ costs, which 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the growers generally pass on to 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 consumers in the form of higher fruit 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 prices. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 C. Consumers generally consider a fruit’s 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 flavor to be important but consider a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fruit’s appearance to be less impor123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 tant. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Chemicals in artificial fertilizers pose 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a health threat to consumers who eat 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fruits produced using artificial 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 fertilizers. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. The use of artificial fertilizers in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 growing fruit has no effect on the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 appearance of the fruit. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 570 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 28–30 are based on the following 26. A recent research study of a particular 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 passage: state’s prison systems indicates that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 prisoners participating in the weekend 6 123456789012345678901234567890121234567890123456789012345678901212345 Line The 35-millimeter (mm) format for 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 furlough program are less likely to become 3456789012345678901234567890121234567890123456789012345678901212345 6 12 movie production became a de facto 3456789012345678901234567890121234567890123456789012345678901212345 6 12 repeat offenders after they are released 3456789012345678901234567890121234567890123456789012345678901212345 6 12 standard around 1913. The mid-1920s 6 123456789012345678901234567890121234567890123456789012345678901212345 than prisoners who do not participate in 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 through the mid-1930s, however, saw a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the program. The study confirms the 3456789012345678901234567890121234567890123456789012345678901212345 6 12 resurgence of wide-film formats. During (5) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 researchers’ hypothesis that weekend 6 123456789012345678901234567890121234567890123456789012345678901212345 this time period, formats used by studios 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 furlough programs at the state’s prisons 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ranged in gauge from 55mm to 70mm. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are an effective means of reducing crime. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Research and development then slack123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Which of the following, if true, would cast ened until the 1950s, when wide-screen 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 the most serious doubt on the hypothesis film-making came back in direct response 6 (10) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to which the last sentence above refers? to the erosion of box-office receipts 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 because of the rising popularity of A. The furlough program was available 6 123456789012345678901234567890121234567890123456789012345678901212345 television. This Cinerama (1952) is 6 123456789012345678901234567890121234567890123456789012345678901212345 only to prisoners who had demon6 123456789012345678901234567890121234567890123456789012345678901212345 generally considered to mark the 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 strated good behavior while in prison. 6 123456789012345678901234567890121234567890123456789012345678901212345 beginning of the modern era of wide(15) 6 123456789012345678901234567890121234567890123456789012345678901212345 B. The crime rate in other states with 6 123456789012345678901234567890121234567890123456789012345678901212345 screen film-making, which saw another 6 123456789012345678901234567890121234567890123456789012345678901212345 similar furlough programs is lower 6 123456789012345678901234567890121234567890123456789012345678901212345 flurry of specialized formats, such as 6 123456789012345678901234567890121234567890123456789012345678901212345 overall than the crime rate in states 6 123456789012345678901234567890121234567890123456789012345678901212345 Cinemascope. In 1956, Panavision 6 123456789012345678901234567890121234567890123456789012345678901212345 without furlough programs. 6 123456789012345678901234567890121234567890123456789012345678901212345 developed Camera 65 for M GM Studios; 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Whether the weekend furlough 6 123456789012345678901234567890121234567890123456789012345678901212345 it was first used during the filming of (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 program is effective depends on how 6 123456789012345678901234567890121234567890123456789012345678901212345 R aintree Country. Panavision soon 6 123456789012345678901234567890121234567890123456789012345678901212345 greatly one values the reform of any 6 123456789012345678901234567890121234567890123456789012345678901212345 contributed another key technical 6 123456789012345678901234567890121234567890123456789012345678901212345 one prisoner. 6 123456789012345678901234567890121234567890123456789012345678901212345 advance by developing spherical 65mm 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Less than half of the prisoners not 6 123456789012345678901234567890121234567890123456789012345678901212345 lenses, which eliminated the “ fat faces” 6 123456789012345678901234567890121234567890123456789012345678901212345 involved in the furlough program 6 123456789012345678901234567890121234567890123456789012345678901212345 syndrome that had plagued earlier (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 become repeat offenders after they are 6 123456789012345678901234567890121234567890123456789012345678901212345 CinemaScope films. 6 123456789012345678901234567890121234567890123456789012345678901212345 released. 6 123456789012345678901234567890121234567890123456789012345678901212345 Some forty “ roadshow” films were E. Less than half of all the prisoners 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 filmed in wide-screen formats during this 6 studied participated in the furlough 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 period. But wide-screen formats flounprogram. 6 123456789012345678901234567890121234567890123456789012345678901212345 dered due to expense, unwieldy cameras, 6 (30) 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and slow film stocks and lenses. After the 6 123456789012345678901234567890121234567890123456789012345678901212345 27. Too many naive consumers hasty and 6 123456789012345678901234567890121234567890123456789012345678901212345 invention of a set of 35mm anamorphic 6 123456789012345678901234567890121234567890123456789012345678901212345 happily provide credit information to 6 123456789012345678901234567890121234567890123456789012345678901212345 lenses, which could be used in conjunc6 123456789012345678901234567890121234567890123456789012345678901212345 unscrupulous merchants, who provide 6 123456789012345678901234567890121234567890123456789012345678901212345 tion with much more mobile cameras to 6 123456789012345678901234567890121234567890123456789012345678901212345 nothing in exchange but a credit fraud 6 123456789012345678901234567890121234567890123456789012345678901212345 squeeze a wide-screen image onto (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 nightmare. 6 123456789012345678901234567890121234567890123456789012345678901212345 theatrical screens, film technology 6 123456789012345678901234567890121234567890123456789012345678901212345 A. hasty and happily provide 6 123456789012345678901234567890121234567890123456789012345678901212345 improved to the point where quality 6 123456789012345678901234567890121234567890123456789012345678901212345 B. hastily and happily provide 6 123456789012345678901234567890121234567890123456789012345678901212345 70mm prints could be blown up from 6 123456789012345678901234567890121234567890123456789012345678901212345 C. hasty and happy providing 6 123456789012345678901234567890121234567890123456789012345678901212345 35mm negatives. 6 123456789012345678901234567890121234567890123456789012345678901212345 D. hastily and happily providing 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. providing hastily and happily 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 571

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 31. M any individuals take antihistamine 28. It can be inferred from the information in 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 medications to alleviate the symptoms of the passage that wide-film formats were 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 allergies. Although all antihistamines are 6 123456789012345678901234567890121234567890123456789012345678901212345 A. in use before 1913. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 essentially similar, there is sufficient 3456789012345678901234567890121234567890123456789012345678901212345 6 12 B. not used during the 1940s. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 variation among the available formulas to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 C. more widely used during the 1920s 6 123456789012345678901234567890121234567890123456789012345678901212345 make some more effective than others for 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 than during the 1930s. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 any particular individual. Therefore, by 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. not used after 1956. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 trying different antihistamine formula6 123456789012345678901234567890121234567890123456789012345678901212345 E. more widely used for some types of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 tions, any allergy sufferer can eventually 3456789012345678901234567890121234567890123456789012345678901212345 6 12 movies than for others. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 find one that is effective. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 29. The passage mentions all the following as 6 123456789012345678901234567890121234567890123456789012345678901212345 Which of the following, if true, would 3456789012345678901234567890121234567890123456789012345678901212345 6 12 factors contributing to the increased use of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most strengthen the conclusion drawn in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 wide-film formats for moviemaking 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the argument above? 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 EXCEPT: 6 123456789012345678901234567890121234567890123456789012345678901212345 A. Antihistamines are the only types of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. spherical camera lenses. medications proven effective in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. Panavision’s Camera 65. treating allergy symptoms. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. television. B. At least one antihistamine will relieve 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. anamorphic camera lenses. any individual’s allergy symptoms. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. movie theater revenues. C. The effectiveness of an antihistamine 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 is partially determined by the drug’s 6 123456789012345678901234567890121234567890123456789012345678901212345 30. Which of the following statements is most 6 123456789012345678901234567890121234567890123456789012345678901212345 specific formulation. 6 123456789012345678901234567890121234567890123456789012345678901212345 strongly supported by the passage’s 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The specific formulation used most 6 123456789012345678901234567890121234567890123456789012345678901212345 information? 6 123456789012345678901234567890121234567890123456789012345678901212345 often by allergy sufferers is not the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 one that would be most effective for A. If a movie does not suffer from the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the greatest number of allergy “ fat faces” syndrome, then it was not 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 sufferers. produced in a wide-film format. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. M ost allergy sufferers experience B. Prior to the invention of the 35mm 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 allergy symptoms that are typical of anamorphic lens, quality larger prints 6 123456789012345678901234567890121234567890123456789012345678901212345 many different types of allergies. 6 123456789012345678901234567890121234567890123456789012345678901212345 could not be made from smaller 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 negatives. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. The same factors that contributed to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the resurgence of wide-film formats in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the 1950s also led to the subsequent 6 123456789012345678901234567890121234567890123456789012345678901212345 decline in their use. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. The most significant developments in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 35mm technology occurred after the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 release of R aintree Country. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. M ovie-theater revenues are not 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 significantly affected by whether the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 movies shown are in wide-screen 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 format. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 1 6 572 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 33. Due to racial discrimination, some of the 6 32. All college students read either literary 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 most gifted and influential jazz musicians 6 classics or current best-selling books as a 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 were prohibited from dining at the venues 6 habit, but some avid readers of current 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 best-selling books do not read literary they have performed in. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 classics as a habit because they do not 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. at the venues they have performed in 6 123456789012345678901234567890121234567890123456789012345678901212345 appreciate these books. People who enjoy 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. at the very same venues they have 3456789012345678901234567890121234567890123456789012345678901212345 6 12 classical music do not find current 3456789012345678901234567890121234567890123456789012345678901212345 6 12 performed in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 best-selling books interesting, and 6 123456789012345678901234567890121234567890123456789012345678901212345 C. where they have performed 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 therefore do not read them as a habit. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. at the same venues at which they 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Since Javier is a college student who 3456789012345678901234567890121234567890123456789012345678901212345 6 12 performed 6 123456789012345678901234567890121234567890123456789012345678901212345 enjoys classical music, he must appreciate 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 E. in venues, which were where they 3456789012345678901234567890121234567890123456789012345678901212345 6 12 literary classics. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 performed 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Which of the following must be true for 3456789012345678901234567890121234567890123456789012345678901212345 6 12 34. In asserting that a thing is honorable, a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the conclusion drawn above to be logically 3456789012345678901234567890121234567890123456789012345678901212345 6 12 favorable distinction is bestowed upon it. correct? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. a favorable distinction is bestowed A. Literary classics are more interesting 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 upon it than current best-selling books. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. we bestow a distinction upon it B. All college students who appreciate 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 favorably literary classics read them as a habit. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. we bestow upon it a favorable C. Literary classics are more interesting 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 distinction than classical music. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. a favorable distinction upon it is D. All avid readers of literary classics 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 bestowed appreciate this type of book. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 E. bestowing a favorable distinction 123456789012345678901234567890121234567890123456789012345678901212345 E. All college students who find classical 6 123456789012345678901234567890121234567890123456789012345678901212345 upon it 6 123456789012345678901234567890121234567890123456789012345678901212345 music enjoyable also read current 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 best-selling books as a habit. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 573

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Questions 36–39 are based on the following 35. A proposed law would prohibit any 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 passage: individual who has been employed as a 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 lobbyist on behalf of a particular industry 6 123456789012345678901234567890121234567890123456789012345678901212345 Line In 1930, a century after the birth of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 from serving as the director of a govern3456789012345678901234567890121234567890123456789012345678901212345 6 12 Victorian poetess Christina Rossetti, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ment agency charged with regulating that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 writer and scholar Virginia Woolf 6 123456789012345678901234567890121234567890123456789012345678901212345 same industry. The purpose of the 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 identified her as “ one of Shakespeare’s 3456789012345678901234567890121234567890123456789012345678901212345 6 12 proposed law is to prevent conflicts of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 (5) more recent sisters” whose life had been 3456789012345678901234567890121234567890123456789012345678901212345 6 12 interest. H owever, if passed, the law 6 123456789012345678901234567890121234567890123456789012345678901212345 reclusively Victorian but whose artistic 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 would prove counterproductive because it 3456789012345678901234567890121234567890123456789012345678901212345 6 12 achievement was enduring. Woolf 3456789012345678901234567890121234567890123456789012345678901212345 6 12 would prevent individuals who are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 remembered Rossetti for the explosive 6 123456789012345678901234567890121234567890123456789012345678901212345 knowledgeable about industries from 2 3456789012345678901234567890121234567890123456789012345678901212345 1 originality, vivid imagery, and emotional 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 serving as government regulators. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 energy of her poems. “ A Birthday,” for (10) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The argument above depends most instance, is no typical Victorian poem 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 directly on which the following assumpand is certainly unlike predictable works 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 tions? of the era’s best-known women poets. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Rossetti’s most famous poem, “ Goblin 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 A. The individuals in government that 6 123456789012345678901234567890121234567890123456789012345678901212345 M arket,” is at once Christian, psycho(15) 6 123456789012345678901234567890121234567890123456789012345678901212345 hold the power to enact the proposed 6 123456789012345678901234567890121234567890123456789012345678901212345 logical, and pro-feminist. Like many of 6 123456789012345678901234567890121234567890123456789012345678901212345 law are susceptible to influence on the 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti’s works, it is extraordinarily 6 123456789012345678901234567890121234567890123456789012345678901212345 part of industry lobbyists. 6 123456789012345678901234567890121234567890123456789012345678901212345 original, risky in subject matter, and 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Government has a legitimate role to 6 123456789012345678901234567890121234567890123456789012345678901212345 unorthodox in form. Its Christian 6 123456789012345678901234567890121234567890123456789012345678901212345 play in the regulation of most 6 123456789012345678901234567890121234567890123456789012345678901212345 allusions are obvious but grounded in (20) 6 123456789012345678901234567890121234567890123456789012345678901212345 industries. 6 123456789012345678901234567890121234567890123456789012345678901212345 opulent images whose lushness borders 6 123456789012345678901234567890121234567890123456789012345678901212345 C. O nly individuals who have served as 6 123456789012345678901234567890121234567890123456789012345678901212345 on the erotic. 6 123456789012345678901234567890121234567890123456789012345678901212345 lobbyists on behalf of an industry are 6 123456789012345678901234567890121234567890123456789012345678901212345 From Rossetti’s work emerge not 6 123456789012345678901234567890121234567890123456789012345678901212345 knowledgeable about that industry. 6 123456789012345678901234567890121234567890123456789012345678901212345 only emotional force, frequently-ironic 6 123456789012345678901234567890121234567890123456789012345678901212345 D. Those who have served as lobbyists 6 123456789012345678901234567890121234567890123456789012345678901212345 playfulness, and intellectual vigor, but (25) 6 123456789012345678901234567890121234567890123456789012345678901212345 on behalf of an industry are capable 6 123456789012345678901234567890121234567890123456789012345678901212345 also an intriguing, enigmatic quality. 6 123456789012345678901234567890121234567890123456789012345678901212345 of objective, unbiased decisions as 6 123456789012345678901234567890121234567890123456789012345678901212345 “ Winter: M y Secret,” for example, regulators. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 combines these traits along with a very E. The primary objective of government 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 high (and un-Victorian) level of poetic regulation of industry should be to 6 123456789012345678901234567890121234567890123456789012345678901212345 self-consciousness. “ H ow does one (30) 6 123456789012345678901234567890121234567890123456789012345678901212345 strengthen and support that industry. 6 123456789012345678901234567890121234567890123456789012345678901212345 reconcile the aesthetic sensuality of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti’s poetry with her repressed, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 ascetic lifestyle?” Woolf wondered. That 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti did indeed withhold a “ secret” 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 both from those intimate with her and (35) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from posterity is Lorna Packer’s thesis in 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 her 1963 biography of Rossetti. Packer’s 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 claim that Rossetti’s was a secret of the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 heart has since been disproved through 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the discovery of hundreds of letters by (40) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 574 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 38. The author discusses Packer’s thesis and Rossetti, which reinforce the conven6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 its flaws in order to tional image of her as pious, scrupulously 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 abstinent, and semi-reclusive. 6 123456789012345678901234567890121234567890123456789012345678901212345 A. contrast the sensuality of Rossetti’s 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Yet the passions expressed in 3456789012345678901234567890121234567890123456789012345678901212345 6 12 poetry with the relative starkness of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Rossetti’s love poems do expose the (45) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 her devotional commentary. 6 123456789012345678901234567890121234567890123456789012345678901212345 “ secret” at the heart of both her life and 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. reveal the secret to which Rossetti 3456789012345678901234567890121234567890123456789012345678901212345 6 12 art: a willingness to forego worldly 3456789012345678901234567890121234567890123456789012345678901212345 6 12 alludes in “ Winter: M y Secret.” 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pleasures in favor of an aestheticized 6 123456789012345678901234567890121234567890123456789012345678901212345 C. call into question the authenticity of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 Christian version of transcendent 3456789012345678901234567890121234567890123456789012345678901212345 6 12 recently discovered letters written by 3456789012345678901234567890121234567890123456789012345678901212345 6 12 fulfillment in heaven. The world, for (50) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Rossetti. 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti, is a fallen place, and her work is 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 D. compare Woolf’s understanding of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pervasively designed to convey this 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Rossetti with a recent, more enlight3456789012345678901234567890121234567890123456789012345678901212345 6 12 inescapable truth. The beauty of her 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ened view. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 poetry must be seen, therefore, as an 123456789012345678901234567890121234567890123456789012345678901212345 E. provide a foundation for the author’s 6 6 123456789012345678901234567890121234567890123456789012345678901212345 artistic strategy, a means toward a moral (55) own theory about Rossetti’s life and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 end. work. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 39. Which of the following best expresses the 6 36. All of the following are mentioned in the 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 main idea of the passage? passage as qualities that emerge from 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti’s work EXCEPT: 6 123456789012345678901234567890121234567890123456789012345678901212345 A. N ewly-discovered evidence suggests 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 that Rossetti’s works were misinterA. lush imagery. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 preted by earlier critics and scholars. 6 B. ironic playfulness. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 B. Rossetti can be compared to ShakesC. stark realism. 6 123456789012345678901234567890121234567890123456789012345678901212345 peare both in her private life and in 6 D. unorthodox form. 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the enduring quality of her work. E. intellectual vigor. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 C. Victorian poetry can be properly 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 37. Which of the following statements is most interpreted only by considering the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonably inferable from the passage? personal life of the particular poet. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. The apparent inconsistency between 6 123456789012345678901234567890121234567890123456789012345678901212345 A. “ Winter: M y Secret” is Rossetti’s 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti’s personal life and literary 6 123456789012345678901234567890121234567890123456789012345678901212345 best-known poem. 6 123456789012345678901234567890121234567890123456789012345678901212345 work are explained by Rossetti’s 6 123456789012345678901234567890121234567890123456789012345678901212345 B. Rossetti was not among the best6 123456789012345678901234567890121234567890123456789012345678901212345 poems themselves. 6 123456789012345678901234567890121234567890123456789012345678901212345 known poets during her era. 6 123456789012345678901234567890121234567890123456789012345678901212345 E. Rossetti’s artistic integrity served as a 6 123456789012345678901234567890121234567890123456789012345678901212345 C. The accounts of Rossetti’s life 6 123456789012345678901234567890121234567890123456789012345678901212345 model for later women poets. contained in Packer’s biography of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Rossetti differ from those included in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Woolf’s biography of Rossetti. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 D. Rossetti’s display of poetic self6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 consciousness drew criticism from her 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 contemporaries. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 E. “ Goblin M arket” was published later 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 than “ A Birthday.” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 575

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 41. The ancient Greek states boasted that 40. Everyone agrees that current licensing 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 within their domains word and speech requirements for child care facilities are 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonably necessary to ensure public were free. 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 safety. Current licensing requirements for 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A. within their domains word and speech 3456789012345678901234567890121234567890123456789012345678901212345 6 12 handgun ownership are far less stringent 3456789012345678901234567890121234567890123456789012345678901212345 6 12 were free 6 123456789012345678901234567890121234567890123456789012345678901212345 than those for operating child care 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 B. within its domain word and speech 3456789012345678901234567890121234567890123456789012345678901212345 6 12 facilities. Yet the recent flurry of school 3456789012345678901234567890121234567890123456789012345678901212345 6 12 were free 3456789012345678901234567890121234567890123456789012345678901212345 6 12 shootings by young children using their 6 123456789012345678901234567890121234567890123456789012345678901212345 C. word and speech were within their 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 parents’ handguns shows that handgun 3456789012345678901234567890121234567890123456789012345678901212345 6 12 domains free 3456789012345678901234567890121234567890123456789012345678901212345 6 12 ownership poses a significant potential 3456789012345678901234567890121234567890123456789012345678901212345 6 12 D. within their domains both word as 6 123456789012345678901234567890121234567890123456789012345678901212345 threat to public safety. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 well as speech were free 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 The author is arguing that E. free word and speech were within 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 their domains A. the recent school shootings would not 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 have occurred were it not for lenient 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 handgun ownership laws. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 B. parents of young children should not 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 be allowed to own handguns. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 C. the legal requirements for obtaining a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 license for operating a child care 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 facility are more stringent than those 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 for handgun ownership. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 D. unlicensed child care and unlicensed 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 handgun ownership both pose a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 potential threat to public safety. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 E. it would be reasonable to impose 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 more stringent requirements for 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 handgun ownership. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 576 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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Answers and Explanations See Appendix for score conversion tables to determine your score. Be sure to keep a tally of correct and incorrect answers for each test section.

1234567890123456789012345678901212345678901234567890123456789012123456 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Issue—Evaluation and Scoring 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Evaluate your Issue-Analysis essay on a scale of 1 to 6 (6 being the highest score) according to 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the following five criteria: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 1. Does your essay develop a position on the issue through the use of incisive reasons and 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 persuasive examples? 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Are your essay’s ideas conveyed clearly and articulately? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay maintain proper focus on the issue, and is it well organized? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 structure, vocabulary, and idiom? 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Analysis of an Argument—Evaluation and Scoring 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Evaluate your Argument-Analysis essay on a scale of 1 to 6 (6 being the highest score) according 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 to the following five criteria: 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. Does your essay identify the key features of the argument and analyze each one in a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 thoughtful manner? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. Does your essay support each point of its critique with insightful reasons and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 examples? 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3. Does your essay develop its ideas in a clear, organized manner, with appropriate 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 transitions to help connect ideas? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 4. Does your essay demonstrate proficiency, fluency, and maturity in its use of sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 structure, vocabulary, and idiom? 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. Does your essay demonstrate command of the elements of Standard Written English, 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 including grammar, word usage, spelling, and punctuation? 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The following series of questions, which serve to identify the Argument’s five distinct problems, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 will help you evaluate your essay in terms of criteria 1 and 2. To earn a score of 4 or higher, your 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 essay should identify at least three of these problems and, for each one, provide at least one 6 123456789012345678901234567890121234567890123456789012345678901212345 1 example or counterexample that supports your critique. (Your examples need not be the same 6 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 577

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 as the ones below.) Identifying and discussing at least four of the problems would help earn you 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 an even higher score. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 • Are key characteristics of one group member (Giant Industries) also characteristics of 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the group as a whole (all employers in a certain state)? (Perhaps Giant is not typical of 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the state’s employers, as a group, with respect to either its financial strength or its the 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 average age of its workforce.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 • Does the term “ largest private business” necessarily mean that Giant employs more 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 workers than any other business in the state? (The smaller the workforce at Giant, the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 less likely that Giant is representative of the state’s employers as a group.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 • Doesn’t the prediction’s accuracy require that other future conditions remain un6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 changed? (For example, the argument ignores a possible influx of workers from other 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 states.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 • Would a reduced workforce necessarily result in business failure? (Perhaps businesses 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 will be more profitable by trimming their workforce.) 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 • What is the definition of “ quality of life” ? (The argument’s ultimate prediction depends 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 on this missing definition.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Quantitative Ability 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1. B In combining fractions, you can divide across fractions all variables except a (in the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a 6 123456789012345678901234567890121234567890123456789012345678901212345 • x 5 1. Then, to isolate x on one numerator) and e (in the denominator), leaving 6 123456789012345678901234567890121234567890123456789012345678901212345 e 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 e 6 123456789012345678901234567890121234567890123456789012345678901212345 : side of the equation, multiply both sides by 6 123456789012345678901234567890121234567890123456789012345678901212345 a 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 e a e 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 • • x 51• 6 123456789012345678901234567890121234567890123456789012345678901212345 a e a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 e 6 123456789012345678901234567890121234567890123456789012345678901212345 x5 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2. A Any one of four distinct groups of three women might be selected: A BC, A BD , A CD , 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 or BCD . The probability that the selections will result in any particular one of these 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 123456789012345678901234567890121234567890123456789012345678901212345 groupings is 1 in 4, or . Similarly, any one of three distinct pairs of two men might be 6 6 123456789012345678901234567890121234567890123456789012345678901212345 4 6 123456789012345678901234567890121234567890123456789012345678901212345 selected: X Y , X Z , and Y Z . The probability that the selections will result in any 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 123456789012345678901234567890121234567890123456789012345678901212345 particular one of these pairs is 1 in 3, or . To determine the combined probability, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 1 1 6 123456789012345678901234567890121234567890123456789012345678901212345 multiply one individual probability by the other: 3 5 . 6 123456789012345678901234567890121234567890123456789012345678901212345 4 3 12 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 578 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3. E The question asks you to compare rates of motion, or speeds. To determine a speed, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 you need to know time and distance. Statement (1) provides only M aria’s time, not 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Lupe’s, so it is insufficient alone to answer the question. Statement (2) compares their 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 driving distances, but it provides no information about Lupe’s driving time. Since 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Lupe’s driving time is a critical fact but is missing from both statements, the correct 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 answer is (E). 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 4. A Apply the formula for determining arithmetic mean (A M below), or simple average. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Letting x equal the other number, solve for x : 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Q 1x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 A M 5 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Q 1 x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 PQ 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2PQ 5 Q 1 x 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2PQ 2 Q 5 x 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 5. C Statement (1) alone provides no information about b and is therefore insufficient to 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. Statement (2) alone is also insufficient because is provides two 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 distinct equations in two variables: a 2 b 5 1 and a 2 b 5 21. N ow consider both 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 statements together. Given statement (1), a 5 3, 23. Substituting 3 and 23 for a into 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 each of the two equations that statement (2) suggests yields four possible values for b: 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 2, 24, 4, and 22. Since you now know all possible values for a and b, you can 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 determine the minimum value of |a 1 b|. (The answer to the question is 1.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6. C H ere’s the sequence up to the 12th second: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 0W 1B 2W 3G 4W 5R 6W 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 7B 8W 9 G 10 W 11 R 12 W 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Every time you reach a time divisible by 6, the sequence starts over with W and 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 proceeds: W-B-W-G -W-R . 204 is divisible by 6; hence, starting at the 204th second, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 here are the light’s movements through the 209th second: 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 204 W 205 B 206 W 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 207 G 208 W 209 R 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 As you can see, the movement from the 208th to the 209th second is from white (W ) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 to red (R ). 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 7. D Statement (1) alone is obviously insufficient to answer the question. Considering 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 statement (2) alone, the factored form of the quadratic expression x 2 2 6x 1 9 is 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (x 2 3)(x 2 3). As you can see, the two roots of the equation in statement (2) are the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 same. The only possible value of x is 3. Thus, statement (2) alone suffices to answer 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 579

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 2 8. E Substitute and 2 individually for u in the defined operation b u c 5 u 2 2 u: 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 3 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 4 2 4 6 2 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 c 5 2 5 2 5 2 b 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 9 3 9 9 9 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 4 2 4 6 10 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 b2 c5 1 5 1 5 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3 9 3 9 9 9 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Then add the two results together:. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 2 10 8 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 2 1 5 . 3456789012345678901234567890121234567890123456789012345678901212345 6 12 9 9 9 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 9. D Extend BE to F (as in the diagram below). m∠EFD 5 m∠ A BE 5 40°. m∠FED must 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 be 110° because a triangles amgle measures sum to 180°. Since ∠BED and ∠FED are 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 supplementary, m∠BED 5 70°. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 10. B $54 is 90% of what Kirk collected. Express this as an equation: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 54 5 .90x 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 540 5 9x 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 60 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Kirk collected $60. If each paper sells for 40 cents, the number of paper Kirk sold is. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 600 60 6 123456789012345678901234567890121234567890123456789012345678901212345 5 5 150. 6 123456789012345678901234567890121234567890123456789012345678901212345 .40 4 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 11. A Add the two equations: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 1y5a 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 2 y 5b 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2x 5 a 1 b 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 ~a 1 b! 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2 6 1 6 580 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 12. E Since the figure has 5 sides, the sum of the measures of the angles is 540°: 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 180(5 2 2) 5 540 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 1 The sum of the mesures of the five angles is 540°. Set up an equation, and then solve 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 for x : 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 540 5 x 1 110 1 60 1 120 1 100 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 540 5 x 1 390 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 150 5 x 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 13. A The shelter houses d 1 c animals altogether. O f these animals, d are dogs. That 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 . portion can be expressed as the fraction 3456789012345678901234567890121234567890123456789012345678901212345 6 12 c 1 d 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 14. C Statement (1) establishes the total contributions of Willot and Tilson counties relative 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 to those of Stanton and O sher counties, but the statement provides no additional 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 information about Stanton County’s specific percentage contribution. Statement (1) 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 alone is therefore insufficient to answer the question. Based on statement (2) alone, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Tilson County’s non-subsidized farms must have accounted for 6% of all revenues 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (18% 2 12% ). Accordingly, Stanton County’s non-subsidized farms must have 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 accounted for 9% of all revenues. (The percentages in the leftmost column must total 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 30.) H owever, this information is insufficient to determine Stanton County’s 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 subsidized farm contribution. With statements (1) and (2) together, O sher County’s 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 revenues must total 36% (because statement (2) stipulates that O sher County 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 contributed twice the revenues of Tilson County, which you now know contributed 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 18% of all revenues). At this point, you’ve partially completed the table: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 N ow you can see that Stanton County’s subsidized farms contributed 6% of the total 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 revenues. (Stanton and O sher revenues must account for 50% of the total.) Thus, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 statements (1) and (2) together suffice to answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 15. D Since the smallest circle has a radius of 1, the medium circle has a radius of 2, and, 6 123456789012345678901234567890121234567890123456789012345678901212345 therefore, the diameter of the large circle must be 6, which makes its radius 3. The arc 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 of a semicircle is half the circle’s circumference—that is, pr. So the length of the bound- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 ary of the shaded region is the sum of the arcs of the three semicircles: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 p 1 2p 1 3p 5 6p. 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 581

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 16. C Statement (1) alone is insufficient because you can make several possible equations 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 using the integers 0 through 9. Statement (2) alone is insufficient for the same reason. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Considering statements (1) and (2) together leaves you with only two possibilities for 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 b n :3 4 or 9 2 . Given that am 5 b n , you can now answer the question. The sum of the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 four integers is 3 1 4 1 9 1 2, or 18. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 17. A The total rent is D 1 100, which must be divided by the number of students (M ). 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 18. D Start with 2, then 4, then 6, and so forth (positive even integers), as the value of n. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 Test each value in turn. You’ll find that only the numbers in the following sequence 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 leave a remainder of 1 when divided by 3: {4, 10, 16, . . .}. N otice that the numbers 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 increase by 6 in sequence. N ext, try a few of these numbers as the value of n in each 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 of the five expressions. You’ll find that all but (n 3 2) are divisible by 3. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 19. E First combine the two terms inside the radical using the common denominator b 2 . 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Then remove perfect squares from the radical: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 a2 a2 a2 1a2 2a2 a 6 123456789012345678901234567890121234567890123456789012345678901212345 1 5 5 5 =2 2 2 2 2 6 123456789012345678901234567890121234567890123456789012345678901212345 b b b b b 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 20. C First consider statement (1) alone. If a 5 21, then the two quantities are equal, while 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 if a has any other value less than 0, the two quantities are unequal. Thus, you can 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 easily dismiss statement (1) as insufficient to answer the question. Consider statement 6 123456789012345678901234567890121234567890123456789012345678901212345 3 123456789012345678901234567890121234567890123456789012345678901212345 (2) alone. If 21 , a , 0, then =a , a (and the answer to the question is yes). For 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3 1 1 1 3 6 123456789012345678901234567890121234567890123456789012345678901212345 example, 2 5 2 , which is less than 2 . But, if 0 , a , 1, then =a . a (and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 8 2 8 6 123456789012345678901234567890121234567890123456789012345678901212345 3 1 123456789012345678901234567890121234567890123456789012345678901212345 1 1 6 123456789012345678901234567890121234567890123456789012345678901212345 the answer to the question is no). For example 5 , which is greater than . 6 123456789012345678901234567890121234567890123456789012345678901212345 8 2 8 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Thus, statement (2) does not suffice. Considering both statements together, 21 , a , 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 0. As already noted, under this constraint the answer to the question is always yes. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3 123456789012345678901234567890121234567890123456789012345678901212345 If a , 21, then =a . a (and the answer to the question is no). For example, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 28 5 22, which is greater than 28. = 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 21. B You can solve the problem by trying each answer choice in turn. O r, you can solve the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 problem algebraically. Let x 5 the number of nickels. 30 2 x 5 the number of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 quarters. Convert both expressions to cents: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5x 5 the value of nickels in cents 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 750 2 25x 5 the value of quarters in cents 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The total of these two expressions is 470. Set up the equation, then solve for x : 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5x 1 750 2 25x 5 470 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 220x 5 2280 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 14 6 1 6 582 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 1 22. D The area of any triangle equals 3 base 3 height. Using 7 miles as the base of the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 12 triangle in this problem, the triangle’s height is the north-south (vertical) distance 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 from A to an imaginary line extending west from B. Statement (1) explicitly provides 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the triangle’s height. Statement (2) also provides sufficient information to determine 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 this height. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 2 1 3456789012345678901234567890121234567890123456789012345678901212345 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 As indicated in the figure above, the triangle’s height is 4 miles (3 2 1 4 2 5 5 2 , per the 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Pythagorean theorem). Accordingly, either statement alone suffices to determine the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 3 7 3 4 5 14.) triangle’s area. (The area 5 6 123456789012345678901234567890121234567890123456789012345678901212345 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 23. C N either statement (1) nor (2) alone suffices to answer the question. You still do not 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 know what portion of the remaining computer systems are equipped only with 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 scanners. H owever, both statements together establish that 55% (100% 2 20% 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 25% ) are equipped only with scanners. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 24. B To answer the question, you need to compare Daniel’s rate of work with that of Carl 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 and Todd working together. Statement (1) provides Carl’s rate, but not Todd’s; 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 therefore, statement (1) alone is insufficient to answer the question. Statement (2) 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 provides Carl’s and Todd’s combined rate. By comparing this combined rate with the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 rate of all three working together, you can determine Daniel’s rate. Statement (2) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 alone suffices to answer the question. Although you don’t have to do the math, here’s 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 6 123456789012345678901234567890121234567890123456789012345678901212345 how you would answer the question. All three workers can load of the van in one 6 123456789012345678901234567890121234567890123456789012345678901212345 8 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1 1 1 6 123456789012345678901234567890121234567890123456789012345678901212345 hour. Similarly, Carl and Todd can load of the van in one hour. Subtract from 6 123456789012345678901234567890121234567890123456789012345678901212345 12 12 8 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 3 2 1 1 1 123456789012345678901234567890121234567890123456789012345678901212345 5 2 5 . Daniel can do of the job (loading 6 to obtain Daniel’s rate: 2 6 123456789012345678901234567890121234567890123456789012345678901212345 8 12 24 24 24 24 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 the van) in one hour, so it would take Daniel 24 hours to load the van. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 25. C By definition, the longest possible chord of a circle is equal in length to the circle’s 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 diameter. Thus, the coordinates of R and S allow you to calculate the circle’s diameter 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 and, in turn, its area. Statements (1) and (2) together suffice to answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 26. E This problem requires a bit of trial and error. Given statement (1), a bit of 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 experimenting with a few numbers—e.g., AB 5 43 and AB 5 24—quickly reveals 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that statement (1) alone is insufficient to answer the question: 4 3 3 5 12 (divisible 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 by 4), but BAB (343) is not divisible by 4. 2 3 4 5 8 (divisible by 4), and BAB (424) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 583

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 is also divisible by 4. Similarly, given statement (2), substituting a few different value 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pairs for A and B that satisfy statement (2) quickly reveals that statement (2) alone is 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 insufficient to answer the question. 3 1 6 1 3 5 12 (divisible by 4), but 363 (BAB) is 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 not divisible by 4. 2 1 4 1 2 5 8 (divisible by 4), and 242 is divisible by 4. Even 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 considered together, statements (1) and (2) are insufficient to answer the question. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 For example, the number 242 satisfies both statements (1) and (2) but is not divisible 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 by 4, whereas the number 484 satisfies both statements (1) and (2) and is divisible 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 by 4. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 27. A Given statement (1), you can determine the total number of paperbacks sold: 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 ($.75)(P) 5 $19.50, or P 5 26. Given that 55 books were sold altogether, 29 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 hardback books were sold, and statement (1) alone suffices to answer the question. 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Statement (2) provides no information about the price of either type of book, and 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 therefore alone is insufficient to answer the question. 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 28. D The age group that spent the most time per week watching sports on television was 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the 19–24 year-old group (who spent an average of approximately 6 hours per week 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 watching sports programming). The average hours for all three groups totals 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 approximately 76 (33 1 17 1 22). O f that total, the two groups other than the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 55 6 123456789012345678901234567890121234567890123456789012345678901212345 19 2 24 age group accounted for 55 hours, or about 76% of the total hours for 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 72 6 123456789012345678901234567890121234567890123456789012345678901212345 all three age groups. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 29. D You’re task here is to compare the size of the entertainment portion of the left-hand 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 bar to the combined sizes of the same portion of the other two bars. Size up the ratio 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 visually. The portion on the first chart is a just a bit larger than the other two 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 combined, isn’t it? So you’re looking for a ratio that’s greater than 1:1. You can rule 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 out answer choices (A) and (B). Approximate the height of each three portions: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 13–18 age group: 25 hours 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 19–24 age group: 5 hours 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 25–30 age group: 10 hours 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The ratio in question is 25:15, or 5:3. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 30. A The amount invested at 5% is (10,000 2 x ) dollars. Thus, the income from that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 amount is .05(10,000 2 x ) dollars. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 31. C Based on the definition of a geometric series in the question, all pairs of successive 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 x 28 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 terms must have the same ratio. Thus, 5 . Cross-multiplying, x 2 5 16; hence 6 6 123456789012345678901234567890121234567890123456789012345678901212345 22 x 6 123456789012345678901234567890121234567890123456789012345678901212345 x 5 64. The constant multiple is either 2 or 22. If the second term is 14, the sixth 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 term would be (2 2)(2)(6 21) 5 ( 22)(2)5 5 2 64. If the second term is 24, the sixth 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 term would be (22)(2 2)5 5 64. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 584 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

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www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 32. C This question requires a bit of intuition. The objective is to minimize the unused 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 space in the packing box by turning the smaller boxes on their appropriate sides. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 Align the 2-inch edge of each box along the 18-inch edge of the packing box (9 boxes 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 make up a row). Align the 5-inch side of each box along the 35-inch edge of the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 packing box (7 boxes make up a row). Arranged in this manner with the 18-inch by 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 35-inch face of the packing box as the base, one layer of small boxes 3 inches high 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 includes 63 boxes (9 3 7). Given that the packing box’s third dimension is 19 inches, 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 6 layers of boxes, each 3 inches high, will fit into the packing box, for a total of 378 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 boxes. An unused 1-inch layer remains at the top of the box. (You could reverse the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 alignment of the 2and 3-inch sides and arrive at the same result.) 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 33. E A median is the number that ranks exactly in the middle of the set. To know the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 median here, you would need to know what the six specific values are, not just their 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 range and/or average. 2 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 34. D Statement (1) alone suffices to answer the question. Given that x 5 60, the area of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 60 1 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 each of the two triangles must be less than (or ) of the area of the circle (the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 360 6 6 123456789012345678901234567890121234567890123456789012345678901212345 difference is the region between each triangle and the circle’s circumference). So, the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 1 123456789012345678901234567890121234567890123456789012345678901212345 combined area of the two triangles is less than the area of the circle. Given that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 120 1 123456789012345678901234567890121234567890123456789012345678901212345 x 5 60, m∠A O C 5 120, and the area of the shaded region is exactly (or ) that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 360 3 6 123456789012345678901234567890121234567890123456789012345678901212345 of the circle. Statement (2) alone also suffices to answer the question. Given that the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 length of A B equals the radius, each of the two triangles must be equilateral, and all 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 angles measure 60°. You can now apply the same reasoning as with statement (1) to 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 answer the question. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 35. C The total distance is equal to the distance that one bus traveled plus the distance that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the other bus traveled (to the point where they pass each other). Letting x equal the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 number of hours traveled, you can express the distances that the two buses travel in 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 that time as 48x and 55x . Equate the sum of these distances with the total distance 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 and solve for x : 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 48x 1 55x 5 515 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 103x 5 515 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 55 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The buses will pass each other five hours after 9:30 a.m.—at 2:30 p.m. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 585

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 36. E The expression involves subtraction, so neither the base numbers nor the exponents 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 can be combined. O nly (E) is equivalent to the original expression. To confirm this 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 without using a calculator, factor 7 76 from both terms: 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 76 1 76 77 76 3456789012345678901234567890121234567890123456789012345678901212345 6 12 7 ~7 2 1! 7 ~6! 7 2 7 76 3456789012345678901234567890121234567890123456789012345678901212345 6 12 5 5 5 7 6 123456789012345678901234567890121234567890123456789012345678901212345 6 6 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 37. B The value of Dynaco shares sold plus the value of M icroTron shares sold must be 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 equal to the value of all shares sold. Letting x represent the number of Dynaco shares 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 sold, you can represent the number of M icroTron shares sold by 300 2 x . Set up an 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 equation in which the value of Dynaco shares sold plus the value of M icroTron shares 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 sold equals the total value of all shares sold. Then solve for x : 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 52x 1 36~300 2 x ! 5 40~300! 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 52x 1 10,800 2 36x 5 12,000 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 16x 5 1,200 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 x 5 75 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 The investor has sold 75 shares of Dynaco stock. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Verbal Ability 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 1. B In the original version, the terms following each part of the correlative not only . . . 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 but also are not parallel. The sentence is also awkward. (B) reconstructs the sentence 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 in a clear and concise manner. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 2. E The original sentence (A) is a long sentence fragment with no predicate. (E) completes 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the sentence by reconstructing it. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 3. D The original version contains superfluous words; either the age of or years should be 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 omitted. (D) corrects the original version by omitting the age of. (E) is redundant; 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 either old or in age should be omitted. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 4. D The argument suggests that the company’s improved profitability the year after the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 court judgement was attributable to that judgment. H owever, the mere fact that one 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 event follows the other does not necessarily mean that it was caused by the other 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 event. (D) points out this critical flaw in the argument by recognizing that consumer 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 buying decisions and, in turn, the profitability of product manufacturers, can depend 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 on a variety of possible factors. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 5. A John’s statement does not logically infer, as Jolanda seems to think, that a person 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 must believe in the inevitability of success in order to be successful. (B) is an effective 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rebuttal for John because it points out Jolanda’s apparent reasoning error. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6. B N owhere in the passage does the author mention any power struggles among the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 leaders of the Iroquois nations. Although the first paragraph does refer to a dispute 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 among the Iroquois leaders, the dispute involved the role that the Iroquois should 6 1 6 586 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 play in the American Revolution. Thus, (B) confuses the information in the passage 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 by referring to unrelated details. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 7. C The passage states that Cornplanter was an outspkoken proponent of assimilation 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 and that H andsome Lake was related to Cornplanter as a half-brother. The fact that 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 Lake was responsible for the Iroquois reasserting their national identity is ironic, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 then, in light of Lake’s blood relationship to Cornplanter. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 8. E According to the author, the Q uakers’ introduction of new technology to the Iroquois 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 was partly responsible for the decline of the Iroquois culture in that it contributed to 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the tribe’s loss of national identity. (E) presents a similar situation. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 9. D In the original version, the position of alone suggests improperly that the immigrants 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 are alone. (D) corrects this problem (m ore and greater are both acceptable here). 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 10. B The first and third sentences, considered together, strongly infer the conclusion ex- 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 pressed by (B). Admittedly, the passage does not rule out the possibility that babies who 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 are breast fed during some portion of the first year other than the first three months are 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 more likely than other babies to become obese. H owever, this possible scenario runs 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 completely contrary to the passage information. Thus, despite this remote possibility, 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (B) is the best answer choice. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 11. E The passage’s first sentence implies that a high level of consumer confidence leads to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 increased consumer spending, which in turn leads to depletion of retail inventories. 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 H owever, the passage indicates that, at a time when consumer confidence is great, 6 123456789012345678901234567890121234567890123456789012345678901212345 retail inventories are increasing instead. Each answer choice except (E) provides a 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 logical explanation for this apparent discrepancy. H owever, (E) suggests that an 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 increase in consumer confidence levels should be preceded by decreased business 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 spending, which would tend to decrease, rather than increase, retail inventory levels. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Thus, (E) actually renders the discrepancy more inexplicable. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 12. D In the original version, one being arrested should be replaced either with one from 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 being arrested, with one’s arrest, or with the noun clause one’s being arrested. (N oun 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 clauses take the possessive verb form.) Also, it would more clearly refer to its 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 antecedent the law if it were positioned closer to the antecedent or replaced with the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 antecedent. (D) corrects both problems with the original version. An even better 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 version would include one’s arrest instead of one from being arrested; nevertheless, 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (D) is the best of the five choices. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 13. A The original version is correct; the first clause modifies President M cKinley, and the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 two elements are appropriately juxtaposed to form a clear expression of the intended 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 idea. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 14. D The original version uses the awkward (and improper) rem ains being. Either is still or 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 simply rem ains should be used instead. (D) corrects the problem. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 15. C As the passage indicates, dendrochronological studies involve analyzing tree rings. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 Although the wood from trees might have been used for creating items which are now 6 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 587

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 considered archeological artifacts, the author does not indicate explicitly that tree 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 rings are studied for the purpose of dating such artifacts. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 16. B In the second paragraph, the author mentions (A), (C), (D), and (E) as problems with 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 radiocarbon dating. N owhere in the passage, however, does the author mention any 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 problem involving sample deterioration. 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 17. E In mentioning that a trace element analysis is needed for the geographic source of an 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 obsidian artifact, the author strongly infers that an accounting for specific conditions 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 of the geographic area is needed in order to determine the age of the obsidian artifact 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 by measuring its hydration layer. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 18. A Statement (A), if true, suggests that the removal of the asbestos could endanger the 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 health of the building’s occupants by sending dangerous fibers into the atmosphere. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Since it is possible that this health risk outweighs the health risk of leaving the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 asbestos in place, the statement provides strong support for the conclusion that the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 asbestos should be left in place in the interest of the occupants’ health. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 19. E The argument assumes that union-relations problems are the major cause of the price 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 increase. (E) undermines the logic of the proposed solution by suggesting that another 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 factor—the cost of raw materials—may be more important. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 20. D The original argument essentially demonstrates the following reasoning: 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: If fluorocarbons are emitted, then ozone depletion will occur. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: If fluorocarbons are not emitted, then ozone depletion will not occur. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 You can express this reasoning symbolically as follows: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: If A, then B. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: If not A, then not B. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 The reasoning is fallacious (flawed), because it fails to account for other possible 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 causes of ozone depletion. (B might occur whether or not A occurs.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Choice (D) is the only answer choice that demonstrates the same essential pattern of 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 flawed reasoning. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: If a person with phlebitis takes Anatol, the phlebitis will be controlled. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 Conclusion: If a person does not take Anatol, the phlebitis will not be controlled. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 N ote that (D) begins with the conclusion, whereas the original argument begins with 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 the premise. This fact makes no difference, however, in assessing the reasoning itself. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 588 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 21. C The argument relies on the assumption that consumers are more likely to buy a 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 particular product (or service) if they remember a particular advertisement for it than 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 if they don’t remember. (C) undermines this crucial assumption. Even if consumers 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 remember an advertisement, unless they also remember the particular product 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 12 advertised, they’re no more likely to buy that product than had they not remembered 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the advertisement at all. 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 22. C In the original sentence, the antecedent of that result is unclear. Is it DN A strands or 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 damage to those strands that result from the deployment of enzymes? Also, the use of 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the noun clause m an-m ade tox ins’ invading in a prepositional phrase here is somewhat 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 awkward, albeit grammatically correct. (B) improperly uses that instead of w hich. Also, 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 it is unclear what “ resulting” refers to here—DN A strands or damage to the DN A 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 strands. (C) improves on the awkward use of a noun clause in the first part of the 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 original sentence. The infinitive to rebuild and the phrase as a result clarify the meaning 6 2 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 of the second part of the sentence. In spite of its use of the passive voice (enzym es are 6 6 123456789012345678901234567890121234567890123456789012345678901212345 deployed), (C) is the best version. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 23. A The original version is correct. By omitting rather, (B) obscures the meaning of the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 sentence; the original version is clearer. (C) sets up a faulty parallel between cultural 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 tie and racial. (D) also sets up a faulty parallel—between cultural and a racial one. (E) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 also sets up a faulty parallel—between cultural and a racial tie. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 24. E The original sentence (A) confuses the subjunctive verb form (which deals with 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 possibilities rather than facts) and past-perfect tense. (A) also contains a pronoun- 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 antecedent agreement problem; scientific com m unity is singular, calling for the 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 singular pronoun it rather than they. (E) remedies both problems. It uses the 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 subjunctive form consistently—at both the beginning and end of the phrase. It also 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 replaces the incorrect plural pronoun they with scientists. 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 25. C The argument recommends that fruit growers not use artificial fertilizers if they wish 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 to appeal to consumer tastes because these fertilizers diminish flavor. This 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 recommendation depends on the assumption that flavor enhances a fruit’s appeal to 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 consumers. Statement (C) helps substantiate this assumption. (Presumably, flavorful 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 fruit is more appealing than flavorless fruit.) 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 26. A The argument relies on the assumption that the furlough program is responsible for, 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 or at least contributes to, a prisoner’s refraining from committing crimes after release. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 O ne effective way of weakening the argument is to refute this assumption by 6 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 providing evidence that the program does not contribute to the reform of prisoners. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 (A) provides strong evidence to this effect—specifically, that program participants are 6 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 less likely than non-participants to commit crimes upon their release, regardless of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 their participation in the program. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 27. B The original sentence (A) improperly uses the adjective hasty instead of the adverb 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 hastily to modify the verb provide. (B) remedies the problem. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 589

Part V: T hree Practice Tests

1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 28. A The passage refers to the establishment of a de facto 35mm standard around 1913, 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 followed by a “ resurgence” of wide-film formats (in the mid-1920s to the 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 mid-1930s). This resurgence suggests that wide-film formats were not new because 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 they had been used before the 35mm standard was established—that is, before 1913. 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 29. D According to the passage’s last sentence, anamorphic lenses, used with more mobile 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 cameras, made it possible to create quality 70mm prints from 35mm negatives. In this 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 respect, the invention of the anamorphic camera lens contributed to the demise (not 3456789012345678901234567890121234567890123456789012345678901212345 6 12 6 123456789012345678901234567890121234567890123456789012345678901212345 the increased use) of wide-film moviemaking. 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 30. B The passage’s final sentence states that after the invention of the 35mm anamorphic 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 lens, quality 70mm (larger) prints could be made from 35mm (smaller) negatives. It is 6 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 3456789012345678901234567890121234567890123456789012345678901212345 12 reasonable to assume that larger prints could not be made from smaller negatives 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 prior to that invention. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 2 3456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 31. B The argument relies on the assumption that every allergy sufferer can be helped by 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 one or another antihistamine. (B) substantiates this necessary assumption. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 32. D Based on the passage’s premise, we can conclude that Javier reads literary classics. In 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 order to also conclude that Javier appreciates literary classics, we must assume that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 all readers of literary classics appreciate these types of books. (D) provides the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 additional premise needed to draw that conclusion. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 33. D The original version incorrectly mixes the past tense (w ere prohibited) with the present 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 perfect tense (have perform ed), resulting in confusion as to the proper time frame. 6 6 123456789012345678901234567890121234567890123456789012345678901212345 Also, ending the sentence with a preposition (in), although not grammatically incor- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 rect, is somewhat awkward and should be avoided if possible. (D) corrects both prob- 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 lems, as well as clarifying the meaning of the sentence by adding the word sam e. (E) is 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 awkward and distorts the meaning of the original sentence by suggesting that these 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 musicians were prohibited from dining at any “ venue” and that “ venues” were the 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 only places they performed. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 34. C The original version includes a dangling modifier. The sentence fails to refer to 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 whomever is doing the asserting. The original version also uses the awkward passive 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 voice. (C) corrects both problems. The first clause now refers clearly to w e, and the 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 underlined clause has been reconstructed using the active voice. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 35. C The argument’s conclusion, stated in the passage’s final sentence, is true only if it is 6 123456789012345678901234567890121234567890123456789012345678901212345 also true that the government has no other choice but to turn to former industry 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 lobbyists if it wants to find knowledgeable regulators. (This is the assumption that 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 (C) provides.) If such people are available elsewhere—for example, among university 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 professors—then the conclusion is faulty. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 36. C In describing Rossetti’s work, the author never uses the words “ stark” or “ realism,” 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 nor does the author describe her work in any way that might be expressed by either of 6 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 these terms. (The term “ vivid imagery,” appearing in line 9, does not carry the same 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 meaning as “ stark realism.” ) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 590 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456

www.petersons.com

TEST 3 1234567890123456789012345678901212345678901234567890123456789012123456 123456789012345678901234567890121234567890123456789012345678901212345 6 6 123456789012345678901234567890121234567890123456789012345678901212345 37. B In lines 10–13, the author states that “ ‘A Birthday’ is no typical Victorian poem and 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 is certainly unlike predictable works of the era’s best-known women poets.” It is 6 3456789012345678901234567890121234567890123456789012345678901212345 12 6 123456789012345678901234567890121234567890123456789012345678901212345 reasonably inferable that Rossetti was not among the era’s best-known women poets, 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 6 1 at least during her time. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 12 38. E The author’s threshold purpose in discussing Packer’s biography is to affirm that 6 6 123456789012345678901234567890121234567890123456789012345678901212345 2 3456789012345678901234567890121234567890123456789012345678901212345 1 Rossetti’s style of writing was not a reflection of her personal lifestyle. H aving dis- 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 missed the theory that Rossetti was keeping secrets about her life, the author goes on 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 (in the final paragraph) to offer a better explanation for the apparent contradiction 6 6 123456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 6 12 between Rossetti’s lifestyle and the emotional, sensual style of her poetry. 3456789012345678901234567890121234567890123456789012345678901212345 6 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 123456789012345678901234567890121234567890123456789012345678901212345 39. D In the passage, the author’s first concern is to point out that Rossetti’s work conflicts 6 2 6 1 3456789012345678901234567890121234567890123456789012345678901212345 3456789012345678901234567890121234567890123456789012345678901212345 12 with her apparently conservative personal life. The author’s own impressions of 6 3456789012345678901234567890121234567890123456789012345678901212345 6 12 Rossetti’s work are corroborated by those of Woolf. Then, in the second paragraph, 6 3456789012345678901234567890121234567890123456789012345678901212345 12 3456789012345678901234567890121234567890123456789012345678901212345 6 12 the author asks how to reconcile this apparent conflict. (The newly discovered letters 6 2 3456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 discussed in that paragraph only reinforce the inconsistency between her personal life 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 and literary work.) In the last paragraph, the author attempts to explain the 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 inconsistency by way of Rossetti’s love poems. (D) nicely embraces all these ideas. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 40. E The argument boils down to the following: 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: Child care license requirements are reasonable because they ensure 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 public safety. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Prem ise: H andgun ownership laws are not as stringent as child care license laws. 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Interm ediate Conclusion: Current handgun ownership laws do not ensure public 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 safety. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 Final conclusion: M ore stringent handgun ownership laws would be reasonable. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 (E) expresses the argument’s final conclusion. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 41. A The original version is clear and grammatically correct. (B) incorrectly uses the 6 123456789012345678901234567890121234567890123456789012345678901212345 singular form its; the verb should agree in number with its plural subject states. (C) 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 awkwardly splits the grammatical element w ere free. (D) uses the redundant and 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 improper correlative both . . . as w ell as . . . (E) confuses the meaning of the sentence; 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the construction unfairly suggests that free word and speech could be found only in 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 the Greek states. 6 123456789012345678901234567890121234567890123456789012345678901212345 123456789012345678901234567890121234567890123456789012345678901212345 66 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 123456789012345678901234567890121234567890123456789012345678901212345 6 1 6 123456789012345678901234567890121234567890123456789012345678901212345 1234567890123456789012345678901212345678901234567890123456789012123456 591

PART

VI Appendix Determining Your Score

594

PART VI

Determining Your Score 123456789012345678901234567890121234567890123456789012 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Determining Your Verbal, Quantitative, and 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Total Scaled Scores 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 To determine your scaled score for either the Q uantitative or Verbal 2345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 section of the practice tests, follow these steps: 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 1: Determine your total number of correct responses for the section, 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 based on the answer explanations. This is your raw score. 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Corrected Raw Score 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Corrected Raw Corrected Raw 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Score Verbal Quantitative Score Verbal Quantitative 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 31 27 19 — 52 41 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 30 25 18 — 51 40 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 28 24 17 — 50 39 2 12345678901234567890123456789012123456789012345678901 27 23 16 — 48 38 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 25 22 15 53 47 37 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 24 21 14 52 46 36 2 12345678901234567890123456789012123456789012345678901 23 20 13 51 45 35 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 22 19 12 50 44 34 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 21 18 11 49 43 33 2 12345678901234567890123456789012123456789012345678901 20 17 10 48 42 32 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 18 16 9 47 41 31 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 17 15 8 45 39 30 2 12345678901234567890123456789012123456789012345678901 16 14 7 44 38 29 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 14 13 6 43 37 28 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 13 12 5 41 36 27 2 12345678901234567890123456789012123456789012345678901 12 11 4 40 35 26 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 11 10 3 38 33 25 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 10 9 2 37 32 24 2 12345678901234567890123456789012123456789012345678901 9 8 1 36 31 23 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 8 7 0 34 30 22 2 12345678901234567890123456789012123456789012345678901 2 33 29 21 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 32 28 20 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 594

Determining Your Score

123456789012345678901234567890121234567890123456789012 12345678901234567890123456789012123456789012345678901 2 2 12345678901234567890123456789012123456789012345678901 Step 2: Subtract one-quarter point from that total for each incorrect 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 response; round off this number to the nearest integer. The result is your 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 corrected raw score. (This is how the pencil-and-paper GM AT penalizes 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 1 test-takers for incorrect responses.) See “ Corrected Raw Score” table on 2 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 the previous page. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Total Scaled Score (200–800) 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 Corrected Total Corrected Total Corrected Total 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Raw Score Scaled Score Raw Score Scaled Score Raw Score Scaled Score 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 2 2345678901234567890123456789012123456789012345678901 2 1 63 and up 370 19 580 41 800 2 12345678901234567890123456789012123456789012345678901 360 18 570 40 790 62 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 350 17 560 39 780 61 2 12345678901234567890123456789012123456789012345678901 2345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 340 16 550 38 770 60 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 330 15 540 37 760 59 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 330 14 530 36 750 58 2 12345678901234567890123456789012123456789012345678901 320 13 530 35 740 57 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 310 12 520 34 730 56 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 300 11 510 33 720 55 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 290 10 500 32 710 54 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 280 9 490 31 700 53 2 12345678901234567890123456789012123456789012345678901 270 8 480 30 690 52 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 260 7 470 29 680 51 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 250 6 460 28 670 50 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 240 5 450 27 660 49 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 230 4 440 26 650 48 2 12345678901234567890123456789012123456789012345678901 220 3 430 25 640 47 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 310 2 420 24 630 46 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 200 0–1 410 23 620 45 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 400 22 610 44 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 390 21 600 43 2 12345678901234567890123456789012123456789012345678901 380 20 590 42 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 Step 3: To determine your total scaled score, add your two corrected raw 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 scores together and convert the total corrected raw score to a scaled score 2 2 12345678901234567890123456789012123456789012345678901 (200–800) using the “ Total Scaled Score” table. 2 12345678901234567890123456789012123456789012345678901 12345678901234567890123456789012123456789012345678901 22 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 12345678901234567890123456789012123456789012345678901 2 1 2 12345678901234567890123456789012123456789012345678901 123456789012345678901234567890121234567890123456789012 595